ISSN:

1930-5346

eISSN:

1930-5338

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## Advances in Mathematics of Communications

May 2019 , Volume 13 , Issue 2

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**Abstract:**

In this paper, we consider additive circulant graph codes which are self-dual additive

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**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.

*+*[Abstract](3631)

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**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

*+*[Abstract](3999)

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**Abstract:**

In this paper, for any even integer

whose dual function is

where

*+*[Abstract](4553)

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**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

*+*[Abstract](4448)

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**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.

*+*[Abstract](3537)

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**Abstract:**

Let

*+*[Abstract](3377)

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**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.

*+*[Abstract](3450)

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**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

*+*[Abstract](3785)

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**Abstract:**

The public-key operation in multivariate encryption and signature schemes evaluates

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