Some results on linear codes over \(\mathbb {F}_p+u\mathbb {F}_p+u^2\mathbb {F}_p\)

DOI10.1007/S12190-014-0786-1zbMath1332.94098OpenAlexW171452924MaRDI QIDQ2354214

Jian Gao

Publication date: 10 July 2015

Published in: Journal of Applied Mathematics and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12190-014-0786-1

zbMATH Keywords

linear codescyclic codesdual codesGray mapsMacWillams identity

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Cyclic codes (94B15)

Related Items (16)

Construction of LCD and new quantum codes from cyclic codes over a finite non-chain ring ⋮ Constacyclic codes over finite commutative semi-simple rings ⋮ Constacyclic and skew constacyclic codes over a finite commutative non-chain ring ⋮ \(\mathbb{F}\)-valued trace of a finite-dimensional commutative \(\mathbb{F}\)-algebra ⋮ New quantum codes from skew constacyclic codes ⋮ Some results on quadratic residue codes over the ring Fp + vFp + v2Fp + v3Fp ⋮ Quantum codes over \(F_{p}\) from cyclic codes over \(F_{p}[u, v/\langle u^2 - 1\), \(v^3 - v, uv - vu\rangle\)] ⋮ Cyclic codes and \(\lambda_1 + \lambda_2 u + \lambda_3 v + \lambda_4 u v\)-constacyclic codes over \(\mathbb{F}_p + u \mathbb{F}_p + v \mathbb{F}_p + u v \mathbb{F}_p\) ⋮ Constacyclic codes over the ring \(\mathbb {F}_q+v\mathbb {F}_q+v^2\mathbb {F}_q\) and their applications of constructing new non-binary quantum codes ⋮ On codes over \(\mathbb {F}_{q}+v\mathbb {F}_{q}+v^{2}\mathbb {F}_{q}\) ⋮ Cyclic codes over a non-chain ring \(R_{e,q}\) and their application to LCD codes ⋮ On skew cyclic codes over \(F_q+vF_q+v^2F_q\) ⋮ Quantum codes derived from one-generator quasi-cyclic codes with Hermitian inner product ⋮ Quantum codes from the cyclic codes over \(\mathbb {F}_{p}[u,v,w/\langle u^{2}-1,v^{2}-1,w^{2}-1,uv-vu,vw-wv,Wu-uw\rangle \)] ⋮ MacDonald codes over the ring \(\mathbb{F}_p + v\mathbb{F}_p + v^2\mathbb{F}_p\) ⋮ On quantum and LCD codes over the ring \(F_q+vF_q+v^2F_q\)

Cites Work

• Cyclic and constacyclic codes over a non-chain ring
• Structure of codes over the ring \(Z_3[v/\langle v^3 - v\rangle\)]
• A class of constacyclic codes over \(\mathbb F_{p}+v\mathbb F_{p}\) and its Gray image
• Fundamentals of Error-Correcting Codes
• Duality for modules over finite rings and applications to coding theory
• The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
• Some Results on Cyclic Codes Over ${F}_{2}+v{F}_{2}$
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