Zobrazeno 1 - 10
of 436
pro vyhledávání: '"94B15"'
We introduce the notion of logarithmically concave (or log-concave) sequences in Coding Theory. A sequence $a_0, a_1, \dots, a_n$ of real numbers is called log-concave if $a_i^2 \ge a_{i-1}a_{i+1}$ for all $1 \le i \le n-1$. A natural sequence of pos
Externí odkaz:
http://arxiv.org/abs/2410.04412
DNA codes have garnered significant interest due to their utilization in digital media storage, cryptography, and DNA computing. In this paper, we first extend the results of constructing reversible group codes \cite{Cengellenmis} and reversible comp
Externí odkaz:
http://arxiv.org/abs/2409.06519
Let $\mathbb{F}_q$ be the finite field of $q$ elements, where $q=p^{m}$ with $p$ being a prime number and $m$ being a positive integer. Let $\mathcal{C}_{(q, n, \delta, h)}$ be a class of BCH codes of length $n$ and designed $\delta$. A linear code $
Externí odkaz:
http://arxiv.org/abs/2408.06282
Autor:
Dastbasteh, Reza, Larrarte, Olatz Sanz, Martinez, Josu Etxezarreta, iOlius, Antonio deMarti, del Moral, Javier Oliva, Bofill, Pedro Crespo
In this study, we investigate the construction of quantum CSS duadic codes with dimensions greater than one. We introduce a method for extending smaller splittings of quantum duadic codes to create larger, potentially degenerate quantum duadic codes.
Externí odkaz:
http://arxiv.org/abs/2407.07753
Let $p$ be an odd prime and $r,s,m$ be positive integers. In this study, we initiate our exploration by delving into the intricate structure of all repeated-root cyclic codes and their duals with a length of $2^rp^s$ over the finite field $\mathbb{F}
Externí odkaz:
http://arxiv.org/abs/2406.13943
Autor:
Jicheng, Ma, Guiying, Yan
A lot of attention has been paid to the investigation of the algebraic properties of linear codes. In most cases, this investigation involves the determination of required code automorphisms, which are useful for decoders, such as the automorphism en
Externí odkaz:
http://arxiv.org/abs/2406.00678
Let $\mathbb{F}_q$ be the finite field of $q=p^m$ elements where $p$ is a prime and $m$ is a positive integer. This paper considers $(\gamma,\Delta)$-cyclic codes over a class of finite commutative non-chain rings $\mathscr{R}_{q,s}=\mathbb{F}_q[v_1,
Externí odkaz:
http://arxiv.org/abs/2404.01904
In this study, in order to get better codes, we focus on double skew cyclic codes over the ring $\mathrm{R}= \mathbb{F}_q+v\mathbb{F}_q, ~v^2=v$ where $q$ is a prime power. We investigate the generator polynomials, minimal spanning sets, generator ma
Externí odkaz:
http://arxiv.org/abs/2403.16833
Let $a$ and $b$ be two non-zero elements of a finite field $\mathbb{F}_q$, where $q>2$. It has been shown that if $a$ and $b$ have the same multiplicative order in $\mathbb{F}_q$, then the families of $a$-constacyclic and $b$-constacyclic codes over
Externí odkaz:
http://arxiv.org/abs/2403.04600
Autor:
Jitman, Somphong
Linear intersection pairs of linear codes have become of interest due to their nice algebraic properties and wide applications. In this paper, we focus on linear intersection pairs of cyclic codes over finite fields. Some properties of cyclotomic cos
Externí odkaz:
http://arxiv.org/abs/2401.02077