Linear codes over \({\mathbb F}_{q}[u]/(u^s)\) with respect to the Rosenbloom-Tsfasman metric

DOI10.1007/s10623-004-5658-5zbMath1142.94387OpenAlexW2051980253WikidataQ58473857 ScholiaQ58473857MaRDI QIDQ2491255

Siap, Irfan, Mehmet Ozen

Publication date: 29 May 2006

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

Full work available at URL: https://doi.org/10.1007/s10623-004-5658-5

zbMATH Keywords

decodingringsRosenbloom-Tsfasman metric

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Other types of codes (94B60) Cyclic codes (94B15)

Related Items (12)

Repeated-root constacyclic codes of prime power length over \(\frac{\mathbb{F}_{p^m} [u}{\langle u^a \rangle}\) and their duals] ⋮ Cyclic and constacyclic codes over a non-chain ring ⋮ Codes over Galois rings with respect to the Rosenbloom-Tsfasman metric ⋮ One generator quasi-cyclic codes over \(\mathbb F_2 + u\mathbb F_2\) ⋮ Structure of codes over the ring \(Z_3[v/\langle v^3 - v\rangle\)] ⋮ A class of optimal \(p\)-ary codes from one-weight codes over \(\mathbb F_p[u/\langle u^m\rangle\)] ⋮ Niederreiter-Rosenbloom-Tsfasman LCD codes ⋮ Cyclic codes over \(\mathbb F_2[u/(u^4-1)\) and applications to DNA codes] ⋮ Good \(p\)-ary quasic-cyclic codes from cyclic codes over \(\mathbb F_p+ v\mathbb F_p\) ⋮ QUATERNARY CONSTRUCTION OF QUANTUM CODES FROM CYCLIC CODES OVER $\mathbb{F}_4 + u\mathbb{F}_4$ ⋮ The covering problem for finite rings with respect to the RT-metric ⋮ The dual code of any \((\delta + \alpha u^2)\)-constacyclic code over \(\mathbb{F}_{2^m} [u \slash \langle u^4 \rangle\) of oddly even length]

Cites Work

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• Cyclic codes over the integers modulo \(p^m\).
• Applications of coding theory to the construction of modular lattices
• The complete weight enumerator for codes over \(\mathcal M_{n\times s}(R)\)
• Maximum distance codes in Mat\(_{n,s}(\mathbb Z_k)\) with a non-Hamming metric and uniform distributions
• Modular and \(p\)-adic cyclic codes
• Type II codes over F/sub 2/+uF/sub 2/
• Cyclic codes and self-dual codes over F/sub 2/+uF/sub 2/

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