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Yansheng Wu

Publications and source records attributed to Yansheng Wu.

26 records · Page 2Linked to original sources
arXiv2020

Binary LCD Codes and Self-orthogonal Codes via Simplicial Complexes

Due to some practical applications, linear complementary dual (LCD) codes and self-orthogonal codes have attracted wide attention in recent years. In this paper, we use simplicial complexes for construction of an infinite family of binary LCD codes and two infinite families of binary self-orthogonal codes. Moreover, we explicitly determine the weight distributions of these codes. We obtain binary LCD codes which have minimum weights two or three, and we also find some self-orthogonal codes meeting the Griesmer bound. As examples, we also present some (almost) {\it optimal} binary self-orthogonal codes and LCD {\it distance optimal} codes.

cs.IT↗
arXiv2020

Few-weight codes over $\Bbb F_p+u\Bbb F_p$ associated with down sets and their distance optimal Gray image

Let $p$ be an odd prime number. In this paper, we construct $2(2p-3)$ classes of codes over the ring $R=\Bbb F_p+u\Bbb F_p,u^2=0$, which are associated with down sets. We compute the Lee weight distributions of the $2(2p-3)$ classes of codes when the down sets are generated by a single maximal element. Moreover, by using the Gray map of the linear codes over $R$, we find out $2(p-1)$ classes of $p$-ary distance optimal linear codes. Two of them meet the Griesmer bound.

cs.IT↗
arXiv2020

Self-reciprocal and self-conjugate-reciprocal irreducible factors of $x^n-λ$ and their applications

In this paper, we present some necessary and sufficient conditions under which an irreducible polynomial is self-reciprocal (SR) or self-conjugate-reciprocal (SCR). By these characterizations, we obtain some enumeration formulas of SR and SCR irreducible factors of $x^n-λ$, $λ\in \Bbb F_q^*$, over $\Bbb F_q$, which are just open questions posed by Boripan {\em et al} (2019). We also count the numbers of Euclidean and Hermitian LCD constacyclic codes and show some well-known results on Euclidean and Hermitian self-dual constacyclic codes in a simple and direct way.

cs.IT↗
arXiv2019

New quaternary codes derived from posets of the disjoint union of two chains

Based on the generic construction of linear codes, we construct linear codes over the ring $\Bbb Z_4$ via posets of the disjoint union of two chains. We determine the Lee weight distributions of the quaternary codes. Moreover, we obtain some new linear quaternary codes and good binary codes by using the Gray map.

cs.IT↗
arXiv2019

A class of functions with low-valued Walsh spectrum

Let $l\equiv 3\pmod 4$, $l\ne 3$, be a prime, $N=l^2$, $f=\frac{l(l-1)}2$ the multiplicative order of a prime $p$ modulo $N$, and $q=p^f$. In this paper, we investigate the Walsh spectrum of the monomial functions $f(x)={\rm Tr}_{q/p}(x^{\frac{q-1}{l^2}})$ in index two case. In special, we explicitly present the value distribution of the Walsh transform of $f(x)$ if $1+l=4p^h$, where $h$ is a class number of $\Bbb Q(\sqrt{-l})$.

cs.IT↗
arXiv2019

Optimal few-weight codes from simplicial complexes

Recently, some infinite families of binary minimal and optimal linear codes are constructed from simplicial complexes by Hyun {\em et al}. Inspired by their work, we present two new constructions of codes over the ring $\Bbb F_2+u\Bbb F_2$ by employing simplicial complexes. When the simplicial complexes are all generated by a maximal element, we determine the Lee weight distributions of two classes of the codes over $\Bbb F_2+u\Bbb F_2$. Our results show that the codes have few Lee weights. Via the Gray map, we obtain an infinite family of binary codes meeting the Griesmer bound and a class of binary distance optimal codes.

cs.IT↗
arXiv2017

Further factorization of $x^n-1$ over a finite field

Let $\Bbb F_q$ be a finite field with $q$ elements and $n$ a positive integer. Martínez, Vergara and Oliveira \cite{MVO} explicitly factorized $x^{n} - 1$ over $\Bbb F_q$ under the condition of $rad(n)|(q-1)$. In this paper, suppose that $rad(n)\nmid (q-1)$ and $rad(n)|(q^w-1)$, where $w$ is a prime, we explicitly factorize $x^{n}-1$ into irreducible factors in $\Bbb F_q[x]$ and count the number of its irreducible factors.

cs.IT↗