Mass formula for self-dual codes over Z\( _{p^2}\)
type: Item
instance of: scholarly article
title: Mass formula for self-dual codes over Z\( _{p^2}\)
zbMATH Open document ID: 1141.94010
author: Jose Maria P. Balmaceda
author: Rowena Alma L. Betty
author: Fidel Nemenzo
published in: Discrete Mathematics
publication date: 2008-05-29T00:00:00Z
review text: \textit{P. Gaborit} [IEEE Trans. Inf. Theory 42, No. 4, 1222--1228 (1996; Zbl 0854.94013)] found a mass formula, which gives the number of nonequivalent self-dual codes over \(\mathbb{Z}_{4}\). In this paper, the authors build on the method of Gaborit to give a mass formula for self-dual codes over \(\mathbb{Z}_{p^{2}}\), where \(p\) is an odd prime. Using the mass formula, they classify the codes of lengths up to \(n=8\) over the ring \(\mathbb{Z}_{9}, n=7\) over \(\mathbb{Z}_{25}\) and \(n=6\) over \(\mathbb{Z}_{49}\).
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 11T71
zbMATH DE Number: 5280735
zbMATH Keywords: mass formula
zbMATH Keywords: codes over rings
zbMATH Keywords: self-dual code
zbMATH Keywords: classification
reviewed by: Zlatko Varbanov
MaRDI profile type: Publication
full work available at URL: j.disc.2007.08.024
OpenAlex ID: W1993033072
cites work: Type II codes over \(\mathbb{F}_{2^m} + u\mathbb{F}_{2^m}\)
cites work: Modular and \(p\)-adic cyclic codes
cites work: Self-dual codes over the integers modulo 4
cites work: Type II codes over F/sub 2/+uF/sub 2/
cites work: All self-dual Z/sub 4/ codes of length 15 or less are known
cites work: Mass formulas for self-dual codes over Z/sub 4/ and F/sub q/+uF/sub q/ rings
cites work: On the classification of self-dual codes over \(\mathbb F_5\)
cites work: All \(\mathbb{Z}_ 4\) codes of type II and length 16 are known
cites work: Self-dual codes over GF(5)
cites work: Q4146667
cites work: Self-Dual Codes over ${\text{GF}}( 3 )$
cites work: Q5509446
cites work: On the uniqueness of the Golay codes
cites work: Self-dual codes over&lt;tex&gt;GF(7)&lt;/tex&gt;(Corresp.)
cites work: Q4242010
cites work: Two ``dual'' families of nearly-linear codes over \(\mathbb Z_p, p\) odd
DOI: 10.1016/J.DISC.2007.08.024
description: scientific article; zbMATH DE number 5280735