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Designs, Codes and Cryptography

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11-10-2018

Totally decomposed cumulative Goppa codes with improved estimations

Authors: Sergey Bezzateev, Natalia Shekhunova

Published in: Designs, Codes and Cryptography | Issue 2-3/2019

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Abstract

A class of q-ary totally decomposed cumulative \(\varGamma (L,G^{j})\)-codes with \(L=\{ \alpha \in :G(\alpha )\ne 0 \}\) and \(G^{j}=G^{j}(x),\; 1 \le j\le q\), where G(x) is a polynomial totally decomposed in \(GF(q^{m})\), are considered. The relation between different codes from this class is studied. Improved bounds of the minimum distance and dimension are obtained.

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Title: Totally decomposed cumulative Goppa codes with improved estimations
Authors: Sergey Bezzateev
Natalia Shekhunova
Publication date: 11-10-2018
Publisher: Springer US
Published in: Designs, Codes and Cryptography / Issue 2-3/2019
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-018-0566-2

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Totally decomposed cumulative Goppa codes with improved estimations

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