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Advances in Mathematics of Communications (AMC) publishes original research papers of the highest quality in all areas of mathematics and computer science which are relevant to applications in communications technology. For this reason, submissions from many areas of mathematics are invited, provided these show a high level of originality, new techniques, an innovative approach, novel methodologies, or otherwise a high level of depth and sophistication. Any work that does not conform to these standards will be rejected.

Areas covered include coding theory, cryptology, combinatorics, finite geometry, algebra and number theory, but are not restricted to these. This journal also aims to cover the algorithmic and computational aspects of these disciplines. Hence, all mathematics and computer science contributions of appropriate depth and relevance to the above mentioned applications in communications technology are welcome.

More detailed indication of the journal's scope is given by the subject interests of the members of the board of editors.

All papers will undergo a thorough peer reviewing process unless the subject matter of the paper does not fit the journal; in this case, the author will be informed promptly. Every effort will be made to secure a decision in three months and to publish accepted papers within six months.

  • AIMS is a member of COPE. All AIMS journals adhere to the publication ethics and malpractice policies outlined by COPE.
  • Publishes 4 issues a year in February, May, August and November.
  • Publishes online only.
  • Indexed in Science Citation Index E, CompuMath Citation Index, Current Contents/Physics, Chemical, & Earth Sciences, INSPEC, Mathematical Reviews, MathSciNet, PASCAL/CNRS, Scopus, Web of Science, Zentralblatt MATH and dblp: computer science bibliography.
  • Archived in Portico and CLOCKSS.
  • Shandong University is a founding institution of AMC.
  • AMC is a publication of the American Institute of Mathematical Sciences. All rights reserved.

Note: “Most Cited” is by Cross-Ref , and “Most Downloaded” is based on available data in the new website.

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Self-dual additive $ \mathbb{F}_4 $-codes of lengths up to 40 represented by circulant graphs
Ken Saito
2019, 13(2) : 213-220 doi: 10.3934/amc.2019014 +[Abstract](96) +[HTML](37) +[PDF](295.67KB)
Abstract:

In this paper, we consider additive circulant graph codes which are self-dual additive \begin{document}$ \mathbb{F}_4 $\end{document}-codes. We classify all additive circulant graph codes of length \begin{document}$ n = 30, 31 $\end{document} and \begin{document}$ 34 \le n \le 40 $\end{document} having the largest minimum weight. We also classify bordered circulant graph codes of lengths up to 40 having the largest minimum weight.

Comparison analysis of Ding's RLWE-based key exchange protocol and NewHope variants
Xinwei Gao
2019, 13(2) : 221-233 doi: 10.3934/amc.2019015 +[Abstract](88) +[HTML](28) +[PDF](480.46KB)
Abstract:

In this paper, we present a comparison study on three RLWE key exchange protocols: one from Ding et al. in 2012 (DING12) and two from Alkim et al. in 2016 (NewHope and NewHope-Simple). We compare and analyze protocol construction, notion of designing and realizing key exchange, signal computation, error reconciliation and cost of these three protocols. We show that NewHope and NewHope-Simple share very similar notion as DING12 in the sense that NewHope series also send small additional bits with small size (i.e. signal) to assist error reconciliation, where this idea was first practically proposed in DING12. We believe that DING12 is the first work that presented complete LWE & RLWE-based key exchange constructions. The idea of sending additional information in order to realize error reconciliation and key exchange in NewHope and NewHope-Simple remain the same as DING12, despite concrete approaches to compute signal and reconcile error are not the same.

Type-preserving matrices and security of block ciphers
Riccardo Aragona and Alessio Meneghetti
2019, 13(2) : 235-251 doi: 10.3934/amc.2019016 +[Abstract](93) +[HTML](15) +[PDF](428.21KB)
Abstract:

We introduce a new property for mixing layers which guarantees protection against algebraic attacks based on the imprimitivity of the group generated by the round functions. Mixing layers satisfying this property are called non-type-preserving. Our main result is to characterize such mixing layers by providing a list of necessary and sufficient conditions on the structure of their underlying binary matrices. Then we show how several families of linear maps are non-type-preserving, including the mixing layers of AES, GOST and PRESENT. Finally we prove that the group generated by the round functions of an SPN cipher with addition modulo \begin{document}$ 2^n $\end{document} as key mixing function is primitive if its mixing layer satisfies this property.

A new construction of rotation symmetric bent functions with maximal algebraic degree
Sihong Su
2019, 13(2) : 253-265 doi: 10.3934/amc.2019017 +[Abstract](51) +[HTML](23) +[PDF](378.05KB)
Abstract:

In this paper, for any even integer \begin{document}$ n = 2m\ge4 $\end{document}, a new construction of \begin{document}$ n $\end{document}-variable rotation symmetric bent function with maximal algebraic degree \begin{document}$ m $\end{document} is given as

whose dual function is

where \begin{document}$ \overline{x_{i}} = x_{i}\oplus 1 $\end{document} and the subscript of \begin{document}$ x $\end{document} is modulo \begin{document}$ n $\end{document}.

Some classes of LCD codes and self-orthogonal codes over finite fields
Xia Li, Feng Cheng, Chunming Tang and Zhengchun Zhou
2019, 13(2) : 267-280 doi: 10.3934/amc.2019018 +[Abstract](66) +[HTML](27) +[PDF](417.6KB)
Abstract:

Due to their important applications in theory and practice, linear complementary dual (LCD) codes and self-orthogonal codes have received much attention in the last decade. The objective of this paper is to extend a recent construction of binary LCD codes and self-orthogonal codes to the general \begin{document}$ p $\end{document}-ary case, where \begin{document}$ p $\end{document} is an odd prime. Based on the extended construction, several classes of \begin{document}$ p $\end{document}-ary linear codes are obtained. The characterizations of these linear codes to be LCD or self-orthogonal are derived. The duals of these linear codes are also studied. It turns out that the proposed linear codes are optimal in many cases in the sense that their parameters meet certain bounds on linear codes. The weight distributions of these linear codes are settled.

Some new constructions of isodual and LCD codes over finite fields
Fatma-Zohra Benahmed, Kenza Guenda, Aicha Batoul and Thomas Aaron Gulliver
2019, 13(2) : 281-296 doi: 10.3934/amc.2019019 +[Abstract](62) +[HTML](22) +[PDF](410.75KB)
Abstract:

This paper presents some new constructions of LCD, isodual, self-dual and LCD-isodual codes based on the structure of repeated-root constacyclic codes. We first characterize repeated-root constacyclic codes in terms of their generator polynomials and lengths. Then we provide simple conditions on the existence of repeated-root codes which are either self-dual negacyclic or LCD cyclic and negacyclic. This leads to the construction of LCD, self-dual, isodual, and LCD-isodual cyclic and negacyclic codes.

Further results on optimal $ (n, \{3, 4, 5\}, \Lambda_a, 1, Q) $-OOCs
Huangsheng Yu, Feifei Xie, Dianhua Wu and Hengming Zhao
2019, 13(2) : 297-312 doi: 10.3934/amc.2019020 +[Abstract](40) +[HTML](18) +[PDF](422.14KB)
Abstract:

Let \begin{document}$ W = \{w_1, w_2, \cdots, w_r\} $\end{document} be a set of \begin{document}$ r $\end{document} integers greater than 1, \begin{document}$ \Lambda_a = (\lambda_a^{(1)}, \lambda_a^{(2)}, \cdots, \lambda_a^{(r)}) $\end{document} be an \begin{document}$ r $\end{document}-tuple of positive integers, \begin{document}$ \lambda_c $\end{document} be a positive integer, and \begin{document}$ Q = (q_1, q_2, \cdots, q_r) $\end{document} be an \begin{document}$ r $\end{document}-tuple of positive rational numbers whose sum is 1. Variable-weight optical orthogonal code (\begin{document}$ (n, W, \Lambda_a, \lambda_c, Q) $\end{document}-OOC) was introduced by Yang for multimedia optical CDMA systems with multiple quality of service requirements. In this paper, tight upper bounds on the maximum code size of \begin{document}$ (n, \{3, 4, 5\}, \Lambda_a, 1, Q) $\end{document}-OOCs are obtained, and infinite classes of optimal \begin{document}$ (n, \{3, 4, 5\}, \Lambda_a, 1, Q) $\end{document}-OOCs are constructed.

Symmetries of weight enumerators and applications to Reed-Muller codes
Martino Borello and Olivier Mila
2019, 13(2) : 313-328 doi: 10.3934/amc.2019021 +[Abstract](36) +[HTML](13) +[PDF](389.76KB)
Abstract:

Gleason's 1970 theorem on weight enumerators of self-dual codes has played a crucial role for research in coding theory during the last four decades. Plenty of generalizations have been proved but, to our knowledge, they are all based on the symmetries given by MacWilliams' identities. This paper is intended to be a first step towards a more general investigation of symmetries of weight enumerators. We list the possible groups of symmetries, dealing both with the finite and infinite case, we develop a new algorithm to compute the group of symmetries of a given weight enumerator and apply these methods to the family of Reed-Muller codes, giving, in the binary case, an analogue of Gleason's theorem for all parameters.

Constructions of optimal balanced $ (m, n, \{4, 5\}, 1) $-OOSPCs
Wei Li, Hengming Zhao, Rongcun Qin and Dianhua Wu
2019, 13(2) : 329-341 doi: 10.3934/amc.2019022 +[Abstract](94) +[HTML](24) +[PDF](412.45KB)
Abstract:

Kitayama proposed a novel OCDMA (called spatial CDMA) for parallel transmission of 2-D images through multicore fiber. Optical orthogonal signature pattern codes (OOSPCs) play an important role in this CDMA network. Multiple-weight (MW) optical orthogonal signature pattern code (OOSPC) was introduced by Kwong and Yang for 2-D image transmission in multicore-fiber optical code-division multiple-access (OCDMA) networks with multiple quality of services (QoS) requirements. Some results had been done on optimal balanced \begin{document}$ (m, n, \{3, 4\}, 1) $\end{document}-OOSPCs. In this paper, it is proved that there exist optimal balanced \begin{document}$ (2u, 16v, \{4, 5\}, 1) $\end{document}-OOSPCs for odd integers \begin{document}$ u\geq 1 $\end{document}, \begin{document}$ v\geq 1 $\end{document}.

Efficient public-key operation in multivariate schemes
Felipe Cabarcas, Daniel Cabarcas and John Baena
2019, 13(2) : 343-371 doi: 10.3934/amc.2019023 +[Abstract](86) +[HTML](43) +[PDF](3517.4KB)
Abstract:

The public-key operation in multivariate encryption and signature schemes evaluates \begin{document}$ m $\end{document} quadratic polynomials in \begin{document}$ n $\end{document} variables. In this paper we analyze how fast this simple operation can be made. We optimize it for different finite fields on modern architectures. We provide an objective and inherent efficiency measure of our implementations, by comparing their performance with the peak performance of the CPU. In order to provide a fair comparison for different parameter sets, we also analyze the expected security based on the algebraic attack taking into consideration the hybrid approach. We compare the attack's efficiency for different finite fields and establish trends. We detail the role that the field equations play in the attack. We then provide a broad picture of efficiency of MQ-public-key operation against security.

A new almost perfect nonlinear function which is not quadratic
Yves Edel and Alexander Pott
2009, 3(1) : 59-81 doi: 10.3934/amc.2009.3.59 +[Abstract](1499) +[PDF](288.3KB) Cited By(42)
Skew constacyclic codes over Galois rings
Delphine Boucher, Patrick Solé and Felix Ulmer
2008, 2(3) : 273-292 doi: 10.3934/amc.2008.2.273 +[Abstract](1460) +[PDF](247.3KB) Cited By(28)
A survey of perfect codes
Olof Heden
2008, 2(2) : 223-247 doi: 10.3934/amc.2008.2.223 +[Abstract](1680) +[PDF](323.1KB) Cited By(24)
A review of the available construction methods for Golomb rulers
Konstantinos Drakakis
2009, 3(3) : 235-250 doi: 10.3934/amc.2009.3.235 +[Abstract](1320) +[PDF](218.2KB) Cited By(22)
Public key cryptography based on semigroup actions
Gérard Maze, Chris Monico and Joachim Rosenthal
2007, 1(4) : 489-507 doi: 10.3934/amc.2007.1.489 +[Abstract](1627) +[PDF](248.6KB) Cited By(22)
A new family of linear maximum rank distance codes
John Sheekey
2016, 10(3) : 475-488 doi: 10.3934/amc.2016019 +[Abstract](1895) +[PDF](390.1KB) Cited By(19)
On the order bounds for one-point AG codes
Olav Geil, Carlos Munuera, Diego Ruano and Fernando Torres
2011, 5(3) : 489-504 doi: 10.3934/amc.2011.5.489 +[Abstract](1373) +[PDF](378.6KB) Cited By(18)
Efficient implementation of elliptic curve cryptography in wireless sensors
Diego F. Aranha, Ricardo Dahab, Julio López and Leonardo B. Oliveira
2010, 4(2) : 169-187 doi: 10.3934/amc.2010.4.169 +[Abstract](1676) +[PDF](304.4KB) Cited By(17)
Geometric constructions of optimal optical orthogonal codes
T. L. Alderson and K. E. Mellinger
2008, 2(4) : 451-467 doi: 10.3934/amc.2008.2.451 +[Abstract](1404) +[PDF](239.2KB) Cited By(16)
Linear nonbinary covering codes and saturating sets in projective spaces
Alexander A. Davydov, Massimo Giulietti, Stefano Marcugini and Fernanda Pambianco
2011, 5(1) : 119-147 doi: 10.3934/amc.2011.5.119 +[Abstract](1885) +[PDF](566.6KB) Cited By(15)
\begin{document}$np^s$\end{document} over \begin{document}$\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}$\end{document}" >Constacyclic codes of length $np^s$ over $\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}$
Yonglin Cao, Yuan Cao, Hai Q. Dinh, Fang-Wei Fu, Jian Gao and Songsak Sriboonchitta
2018, 12(2) : 231-262 doi: 10.3934/amc.2018016 +[Abstract](1355) +[HTML](364) +[PDF](555.31KB) PDF Downloads(182)
Characterization of extended Hamming and Golay codes as perfect codes in poset block spaces
B. K. Dass, Namita Sharma and Rashmi Verma
2018, 12(4) : 629-639 doi: 10.3934/amc.2018037 +[Abstract](750) +[HTML](338) +[PDF](366.18KB) PDF Downloads(148)
New families of strictly optimal frequency hopping sequence sets
Jingjun Bao
2018, 12(2) : 387-413 doi: 10.3934/amc.2018024 +[Abstract](1303) +[HTML](245) +[PDF](613.0KB) PDF Downloads(128)
\begin{document}$ {{\mathbb{Z}}_{2}}{{\mathbb{Z}}_{2}}{{\mathbb{Z}}_{4}}$\end{document}-additive cyclic codes" >$ {{\mathbb{Z}}_{2}}{{\mathbb{Z}}_{2}}{{\mathbb{Z}}_{4}}$-additive cyclic codes
Tingting Wu, Jian Gao, Yun Gao and Fang-Wei Fu
2018, 12(4) : 641-657 doi: 10.3934/amc.2018038 +[Abstract](658) +[HTML](336) +[PDF](409.5KB) PDF Downloads(116)
Strongly secure quantum ramp secret sharing constructed from algebraic curves over finite fields
Ryutaroh Matsumoto
2019, 13(1) : 1-10 doi: 10.3934/amc.2019001 +[Abstract](397) +[HTML](183) +[PDF](344.95KB) PDF Downloads(110)
Improved attacks on knapsack problem with their variants and a knapsack type ID-scheme
Konstantinos A. Draziotis and Anastasia Papadopoulou
2018, 12(3) : 429-449 doi: 10.3934/amc.2018026 +[Abstract](851) +[HTML](192) +[PDF](543.19KB) PDF Downloads(109)
Indiscreet logarithms in finite fields of small characteristic
Robert Granger, Thorsten Kleinjung and Jens Zumbrägel
2018, 12(2) : 263-286 doi: 10.3934/amc.2018017 +[Abstract](1528) +[HTML](301) +[PDF](541.54KB) PDF Downloads(100)
New constructions of systematic authentication codes from three classes of cyclic codes
Yunwen Liu, Longjiang Qu and Chao Li
2018, 12(1) : 1-16 doi: 10.3934/amc.2018001 +[Abstract](1348) +[HTML](247) +[PDF](422.32KB) PDF Downloads(100)
A class of skew-cyclic codes over $\mathbb{Z}_4+u\mathbb{Z}_4$ with derivation
Amit Sharma and Maheshanand Bhaintwal
2018, 12(4) : 723-739 doi: 10.3934/amc.2018043 +[Abstract](626) +[HTML](479) +[PDF](463.68KB) PDF Downloads(93)
On some classes of codes with a few weights
Yiwei Liu and Zihui Liu
2018, 12(2) : 415-428 doi: 10.3934/amc.2018025 +[Abstract](1031) +[HTML](246) +[PDF](376.9KB) PDF Downloads(89)

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