Advances in Mathematics of Communications
February 2021 , Volume 15 , Issue 1
Select all articles
Two bounds on the minimum distance of cyclic codes are proposed. The first one generalizes the Roos bound by embedding the given cyclic code into a cyclic product code. The second bound also uses a second cyclic code, namely the non-zero-locator code, but is not directly related to cyclic product codes and it generalizes a special case of the Roos bound.
Applied in consumer electronics, communication, data storage system, secret sharing, authentication codes, association schemes, and strongly regular graphs, linear codes attract much interest. We consider the construction of linear codes with two or three weights. Let
can be constructed by a defining set
Golay complementary sets (GCSs) are widely used in different communication systems, i.e., GCSs could be used in OFDM systems to control peak-to-mean envelope power ratio (PMEPR). In this paper, inspired by the work on GCSs with large zero correlation zone given by Chen et al in 2018, we investigate the relationship between GCSs and zero odd-periodic correlation zone (ZOCZ) sequence sets, and present GCSs with flexible sequence set sizes, sequence lengths, large ZOCZ and low PMEPR. Those proposed sequences could be applied in OFDM system for synchronization.
We introduce the Hadamard full propelinear codes that factorize as direct product of groups such that their associated group is
Bent functions have many important applications in cryptography and coding theory. This paper considers a class of
We present a cryptanalysis of a signature scheme HIMQ-3 due to Kyung-Ah Shim et al [
We evaluate the complete weight enumerator of the linear codes
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).
In this work, we propose a post-quantum UC-commitment scheme in the Global Random Oracle Model, where only one non-programmable random oracle is available. The security of our proposal is based on two well-established post-quantum hardness assumptions from coding theory: The Syndrome Decoding and the Goppa Distinguisher. We prove that our proposal is perfectly hiding and computationally binding.
As an application, we investigate the weight distribution of a
where its defining set
In this paper, we give some properties of the cycle decomposition of a nonlinear feedback shift register called WG-NLFSR which was presented by Mandal and Gong recently. First we give the parity of the state transition transformation of WG-NLFSR and then by the relation of the parity of a permutation and its number of cycles given in Theorem 2 in Section 1, we show that the number of cycles in the cycle decomposition of WG-NLFSR is even. Second we study the properties of the cycle decomposition of WG-NLFSR when the coefficients of the characteristic polynomial belong to the proper subfields of the finite field on which the WG-NLFSR is defined. Finally, we give some properties of the cycle decomposition of the filtering WG7-NLFSR.
Add your name and e-mail address to receive news of forthcoming issues of this journal:
[Back to Top]