Related papers: Algebraic Decoding of Negacyclic Codes Over Z_4
We adress the problem of the algebraic decoding of any cyclic code up to the true minimum distance. For this, we use the classical formulation of the problem, which is to find the error locator polynomial in terms of the syndroms of the…
We present a list decoding algorithm for quaternary negacyclic codes over the Lee metric. To achieve this result, we use a Sudan-Guruswami type list decoding algorithm for Reed-Solomon codes over certain ring alphabets. Our decoding…
In this paper, we study negacyclic codes of odd length and of length $2^k$ over the ring $R=\mathbb{Z}_4+u\mathbb{Z}_4$, $u^2=0$. We give the complete structure of negacyclic codes for both the cases. We have obtained a minimal spanning set…
Let $R=\mathbb{Z}_{4}[v]/\langle v^2+2v\rangle=\mathbb{Z}_{4}+v\mathbb{Z}_{4}$ ($v^2=2v$) and $n$ be an odd positive integer. Then $R$ is a local non-principal ideal ring of $16$ elements and there is a $\mathbb{Z}_{4}$-linear Gray map from…
In this paper, we construct a new family of distance-optimal binary cyclic codes with the minimum distance $6$ and a new family of distance-optimal quaternary cyclic codes with the minimum distance $4$. We also construct several families of…
In this paper, an explicit representation and enumeration for negacyclic codes of length $2^kn$ over the local non-principal ideal ring $R=\mathbb{Z}_4+u\mathbb{Z}_4$ $(u^2=0)$ is provided, where $k, n$ are any positive integers and $n$ is…
Let $\mathbb{Z}_4$ denote the ring of integers modulo $4$. The Galois ring GR$(4,m)$, which consists of $4^m$ elements, represents the Galois extension of degree $m$ over $\mathbb{Z}_4$. The constructions of codes over $\mathbb{Z}_4$ have…
Negacyclic BCH codes are an important subclass of negacyclic codes and are the best linear codes in most cases, but their parameters are hard to determine. In this paper, we mainly study two types of negacyclic BCH codes of length…
We study constacyclic codes, of length $np^s$ and $2np^s$, that are generated by the polynomials $(x^n + \gamma)^{\ell}$ and $(x^n - \xi)^i(x^n + \xi)^j$\ respectively, where $x^n + \gamma$, $x^n - \xi$ and $x^n + \xi$ are irreducible over…
A new lower bound on the minimum Hamming distance of linear quasi-cyclic codes over finite fields is proposed. It is based on spectral analysis and generalizes the Semenov- Trifonov bound in a similar way as the Hartmann-Tzeng bound extends…
Repeated root Cyclic and Negacyclic codes over Galois rings have been studied much less than their simple root counterparts. This situation is beginning to change. For example, repeated root codes of length $p^s$, where $p$ is the…
Binary cyclic codes having large dimensions and minimum distances close to the square-root bound are highly valuable in applications where high-rate transmission and robust error correction are both essential. They provide an optimal…
Negacyclic BCH codes are a subclass of neagcyclic codes and are the best linear codes in many cases. However, there have been very few results on negacyclic BCH codes. Let $q$ be an odd prime power and $m$ be a positive integer. The…
In this paper we study spread codes: a family of constant-dimension codes for random linear network coding. In other words, the codewords are full-rank matrices of size (k x n) with entries in a finite field F_q. Spread codes are a family…
Reed--Solomon error-correcting codes are ubiquitous across computer science and information theory, with applications in cryptography, computational complexity, communication and storage systems, and more. Most works on efficient error…
We present new upper and lower bounds on the minimum distance of certain generalized bicycle (GB) codes beyond the reach of techniques for classical codes capable of even capturing the true minimum distance for some cases. These bounds are…
In this paper, by investigating the factor of the $x^n+1$, we deduce that the structure of the reversible negacyclic code over the finite field $\mathbb{F}_{q}$, where $q$ is an odd prime power. Though studying $q-$cyclotomic cosets modulo…
Let $\mathbb{F}_p$ denote the finite field of order $p$, where $p$ is an odd prime. We study certain quantum negacyclic codes over $\mathbb{F}_p$ which we call $t$-Frobenius negacyclic codes. We obtain a criterion for constructing such…
We propose a new algorithm for decoding Reed-Solomon codes (up to half the minimum distance) and for computing inverses in $F[x]/m(x)$. The proposed algorithm is similar in spirit and structure to the Berlekamp-Massey algorithm, but it…
The paper presents a comprehensive study of group codes from non-abelian split metacyclic group algebras. We derive an explicit Wedderburn-like decomposition of finite split metacyclic group algebras over fields with characteristic coprime…