# American Institute of Mathematical Sciences

ISSN:
1930-5346

eISSN:
1930-5338

All Issues

## Advances in Mathematics of Communications

Open Access Articles

2019, 0(0): 0-0 doi: 10.3934/amc.2020045 +[Abstract](395) +[HTML](191) +[PDF](337.74KB)
Abstract:

We investigate a class of linear codes by choosing a proper defining set and determine their complete weight enumerators and weight enumerators. These codes have at most three weights and some of them are almost optimal so that they are suitable for applications in secret sharing schemes. This is a supplement of the results raised by Wang et al. (2017) and Kong et al. (2019).

2019, 0(0): 0-0 doi: 10.3934/amc.2020021 +[Abstract](695) +[HTML](331) +[PDF](299.89KB)
Abstract:

McNie [8] is a code-based public key encryption scheme submitted to the NIST Post-Quantum Cryptography standardization [10] as a candidate. In this paper, we present Dual-Ouroboros, an improvement of McNie, which can be seen as a dual version of the Ouroboros-R protocol [1], another candidate to the NIST competition. This new improved protocol permits, first, to avoid an attack proposed by Gaborit [7] and second permits to benefit from a reduction security to a standard problem (as the original Ouroboros protocol).

2019, 0(0): 0-0 doi: 10.3934/amc.2020020 +[Abstract](614) +[HTML](303) +[PDF](504.29KB)
Abstract:

This paper is concerned with the construction of algebraic-geometric (AG) codes defined from GGS curves. It is of significant use to describe bases for the Riemann-Roch spaces associated with some rational places, which enables us to study multi-point AG codes. Along this line, we characterize explicitly the Weierstrass semigroups and pure gaps by an exhaustive computation for the basis of Riemann-Roch spaces from GGS curves. In addition, we determine the floor of a certain type of divisor and investigate the properties of AG codes. Multi-point codes with excellent parameters are found, among which, a presented code with parameters \begin{document}$[216,190,\geqslant 18]$\end{document} over \begin{document}$\mathbb{F}_{64}$\end{document} yields a new record.

2015, 9(1): 9-21 doi: 10.3934/amc.2015.9.9 +[Abstract](2823) +[PDF](424.1KB)
Abstract:
In this paper, a novel method for constructing complementary sequence set with zero correlation zone (ZCZ) is presented by interleaving and combining three orthogonal matrices. The constructed set can be divided into multiple sequence groups and each sequence group can be further divided into multiple sequence subgroups. In addition to ZCZ properties of sequences from the same sequence subgroup, sequences from different sequence groups are orthogonal to each other while sequences from different sequence subgroups within the same sequence group possess ideal cross-correlation properties, that is, the proposed ZCZ sequence set has inter-group orthogonal (IGO) and inter-subgroup complementary (ISC) properties. Compared with previous methods, the new construction can provide flexible choice for ZCZ width and set size, and the resultant sequences which are called IGO-ISC sequences in this paper can achieve the theoretical bound on the set size for the ZCZ width and sequence length.

2018  Impact Factor: 0.879