Computing Efficiently a Parity-Check Matrix for Zps-Additive Codes
Journal
IEEE Transactions on Information Theory
ISSN
0018-9448
ISSN-Digital
1557-9654
Type
journal article
Date Issued
2024
Author(s)
Abstract
The Zps -additive codes of length n are subgroups of
Z
n
ps , with p prime and s ≥ 1. They can be seen as a generalization
of linear codes over Z2, Z4, or more general over Z2s . In
this paper, we show two methods for computing a parity-check
matrix of a Zps -additive code from a generator matrix of the
code in standard form. We also compare the performance of
our results implemented in Magma with the current available
function in Magma for linear codes over finite rings in general.
Complementing this comparison, we also show a time complexity
analysis of the algorithms. The rings Zps belong to a more general
class of rings: finite chain rings. Along the paper, we observe that
the same results can be applied to any linear code over a finite
commutative chain ring
Z
n
ps , with p prime and s ≥ 1. They can be seen as a generalization
of linear codes over Z2, Z4, or more general over Z2s . In
this paper, we show two methods for computing a parity-check
matrix of a Zps -additive code from a generator matrix of the
code in standard form. We also compare the performance of
our results implemented in Magma with the current available
function in Magma for linear codes over finite rings in general.
Complementing this comparison, we also show a time complexity
analysis of the algorithms. The rings Zps belong to a more general
class of rings: finite chain rings. Along the paper, we observe that
the same results can be applied to any linear code over a finite
commutative chain ring
Funding(s)
10.13039/501100001871-Fundação para a Ciência e a Tecnologia (Grant Number: UIDB/04106/2020)
10.13039/501100003030-Agència de Gestió d'Ajuts Universitaris i de Recerca (Grant Number: 021 SGR 00643)
10.13039/501100003329-Ministerio de Economía y Competitividad (Grant Number: ID2019-104664GB-I00, ID2022-137924NB-I00 and RED2022-134306-T (AEI / 10.13039/501100011033))
Language
English
Keywords
Additive code
chain ring
parity-check matrix
performance
time complexity
HSG Classification
contribution to scientific community
Refereed
Yes
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Official URL
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