On the linearity and classification of \(\mathbb{Z}_{p^s} \)-linear generalized Hadamard codes

DOI10.1007/s10623-022-01026-2zbMath1500.94084OpenAlexW4225530725WikidataQ114849770 ScholiaQ114849770MaRDI QIDQ2119951

Dipak Kumar Bhunia, Mercè Villanueva, Cristina Fernández-Córdoba

Publication date: 31 March 2022

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10623-022-01026-2

zbMATH Keywords

classificationlinear codekerneladditive codeGray mapHadamard code

Mathematics Subject Classification ID

Other types of codes (94B60) Combinatorial codes (94B25)

Related Items (3)

On the constructions of \(\mathbb{Z}_p \mathbb{Z}_{p^2}\)-linear generalized Hadamard codes ⋮ Linearity and classification of \(\mathbb{Z}_p \mathbb{Z}_{p^2} \)-linear generalized Hadamard codes ⋮ Partial permutation decoding and PD-sets for \(\mathbb{Z}_{p^s}\)-linear generalized Hadamard codes

Uses Software

• Magma

Cites Work

• Unnamed Item
• Algebraic techniques for nonlinear codes
• Codes over \(\mathbb{Z}_{2^k}\), Gray map and self-dual codes
• Generalized Hadamard full propelinear codes
• On difference matrices, resolvable transversal designs and generalized Hadamard matrices
• A metric for codes over residue class rings
• Weighted modules and representations of codes
• On \(\mathbb {Z}_{2^s}\)-linear Hadamard codes: kernel and partial classification
• On two-weight \(\mathbb {Z}_{2^k}\)-codes
• Equivalences among \(\mathbb{Z}_{2^s} \)-linear Hadamard codes
• On linear codes over \(\mathbb Z_2\)
• Kernels and \(p\)-kernels of \(p^r\)-ary 1-perfect codes.
• Ranks and Kernels of Codes From Generalized Hadamard Matrices
• Every Z2k-Code is a Binary Propelinear Code
• On the additive (/spl Zopf//sub 4/-linear and non-/spl Zopf//sub 4/-linear) Hadamard codes: rank and kernel
• On $Z_{2^k}$-Dual Binary Codes
• On BCH codes over arbitrary integer tings (Corresp.)
• Codes over integer residue rings
• The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
• On Z₂k -Linear and Quaternary Codes
• Gray isometries for finite chain rings and a nonlinear ternary (36, 3/sup 12/, 15) code
• Z/sub 2/k-linear codes
• The Geometry of Two-Weight Codes Over ℤ_p^m
• On $Z_p Z_{p^k}$ -Additive Codes and Their Duality

This page was built for publication: On the linearity and classification of \(\mathbb{Z}_{p^s} \)-linear generalized Hadamard codes