Results 41 to 50 of about 547 (94)
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
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Quantum Codes as an Application of Constacyclic Codes
AxiomsThe main focus of this paper is to analyze the algebraic structure of constacyclic codes over the ring R=Fp+w1Fp+w2Fp+w22Fp+w1w2Fp+w1w22Fp, where w12−α2=0, w1w2=w2w1, w23−β2w2=0, and α,β∈Fp∖{0}, for a prime p. We begin by introducing a Gray map defined over R, which is associated with an invertible matrix.
Raza, Mohd +8 more
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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
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Several families of irreducible constacyclic and cyclic codes
Designs, Codes and Cryptography, 2023 In this paper, several families of irreducible constacyclic codes over finite fields and their duals are studied. The weight distributions of these irreducible constacyclic codes and the parameters of their duals are settled. Several families of irreducible constacyclic codes with a few weights and several families of optimal constacyclic codes are ...
Zhonghua Sun 0001 +2 more
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Quantum Codes from Galois Hulls of Constacyclic Codes over a Finite Non-Chain Ring
EntropyWe study the algebraic structures of constacyclic codes over a new finite non-chain ring R and their l-Galois dual codes based on a new Gray map ϕ and determine the dimensions of the l-Galois hull of constacyclic codes over R.
Enbin Zhang, Bo Kong, Xiying Zheng
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Constacyclic codes over finite fields
Finite Fields and Their Applications, 2012 An equivalence relation called isometry is introduced to classify constacyclic codes over a finite field; the polynomial generators of constacyclic codes of length $\ell^tp^s$ are characterized, where $p$ is the characteristic of the finite field and $\ell$ is a prime different from $p$.
Bocong Chen +3 more
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The Galois variance of constacyclic codes
Finite Fields and Their Applications, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A q-polynomial approach to constacyclic codes
Finite Fields and Their Applications, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Weijun Fang +2 more
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New quantum codes from skew constacyclic codes
Advances in Mathematics of Communications, 2023 In the paper under review, the authors construct quantum codes from skew constacyclic codes over the finite commutative non-chain ring of order \(p^{2^{\ell} m}\) with characteristic odd prime \(p\): \[ R_{\ell,m} = \mathbb{F}_{p^m}[v_1,v_2,\dots,v_{\ell}]/\langle v^2_i-1, v_iv_j-v_jv_i\rangle_{1\leq i, j\leq \ell}, \] where \(m\) and \(\ell\) are ...
Ram Krishna Verma +3 more
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Structure and Enumeration of Constacyclic Codes over Cube-Zero Local Rings of Order q5
MathematicsWe investigate λ-constacyclic codes of length n over finite commutative local rings R of characteristic p and order q5, where q=pm is an odd prime power, whose Jacobson radical N satisfies N3=0≠N2, under the coprimality condition gcd(n,p)=1.
Sami H. Saif, Shayea Aldossari
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