Results 41 to 50 of about 1,030 (123)
On Gray Images of Constacyclic Codes
ITM Web of Conferences, 2018 This paper deals with constacyclic codes over a new ring. Gray images of these codes over those rings are obtained. The relations between these codes and their Gray images are given.
Özkan Mustafa, Öke Figen
doaj +1 more source
On Linear Perfect b-Symbol Codes over Finite Fields
Mathematics, 2023 Motivated by the application of high-density data storage technologies, Cassuto and Blaum introduced codes for symbol-pair read channels in 2011, and Yaakobi et al. generalized the coding framework to that for b-symbol read channels where b≥2 in 2016. In
Kanat Abdukhalikov +2 more
doaj +1 more source
Quantum MDS Codes over Small Fields
, 2015 We consider quantum MDS (QMDS) codes for quantum systems of dimension $q$ with lengths up to $q^2+2$ and minimum distances up to $q+1$. We show how starting from QMDS codes of length $q^2+1$ based on cyclic and constacyclic codes, new QMDS codes can be ...
Grassl, Markus, Roetteler, Martin
core +1 more source
DNA codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022 A one to one correspondence between the elements of a finite local Frobenius non-chain ring of length 5 and nilpotency index 4, and k-tuples of DNA codewords is established.
Castillo-Guillén C. A. +1 more
doaj +1 more source
Polycyclic codes over Galois rings with applications to repeated-root constacyclic codes
, 2012 Cyclic, negacyclic and constacyclic codes are part of a larger class of codes called polycyclic codes; namely, those codes which can be viewed as ideals of a factor ring of a polynomial ring.
Lopez-Permouth, Sergio R. +3 more
core +1 more source
Finite Fields and Their Applications, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +2 more sources
Skew constacyclic codes over Galois rings
Advances in Mathematics of Communications, 2008 We generalize the construction of linear codes via skew polynomial rings by using Galois rings instead of finite fields as coefficients. The resulting non commutative rings are no longer left and right Euclidean. Codes that are principal ideals in quotient rings of skew polynomial rings by a two sided ideals are studied.
Boucher, Delphine +2 more
openaire +2 more sources
On the construction of constacyclically permutable codes from constacyclic codes
AIMS Mathematics<abstract><p>In this paper, we propose a way to partition any constacyclic code over a finite field in its equivalence classes according to the algebraic structure of the code. Such a method gives the generalization of cyclically permutable codes (CPCs), which are called constacyclically permutable codes (CCPCs), and it is useful to derive ...
Guanghui Zhang, Shuhua Liang
openaire +2 more sources
Constacyclic codes over 𝔽q𝒮𝒯 and their applications
AKCE International Journal of Graphs and CombinatoricsLet [Formula: see text], where p is an odd prime and r is a positive integer. Consider a ring [Formula: see text], where [Formula: see text] with [Formula: see text] and [Formula: see text] with [Formula: see text].
Amal S. Alali +3 more
doaj +1 more source
Constacyclic codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020 The family of finite local Frobenius non-chain rings of length 5 and nilpotency index 4 is determined, as a by-product all finite local Frobenius non-chain rings with p5 elements (p a prime) and nilpotency index 4 are given.
Castillo-Guillén C. A. +1 more
doaj +1 more source