$The structure of one weight linear and cyclic codes over Z_{2}^r x (Z_{2} + uZ_{2})^s$

The structure of one weight linear and cyclic codes over Z_{2}^r x (Z_{2} + uZ_{2})^s

Inspired by the Z2Z4-additive codes, linear codes over Z_{2}^r x (Z_{2} + uZ_{2})^s have been introduced by Aydogdu et al. more recently. Although these family of codes are similar to each other, linear codes over Z_{2}^r x (Z_{2} + uZ_{2})^s have some advantages compared to Z2Z4-additive codes....

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Main Author:	Ismail Aydogdu
Format:	Article
Language:	English
Published:	Balikesir University 2017-12-01
Series:	An International Journal of Optimization and Control: Theories & Applications
Subjects:	One weight codes Z2Z2[u]-linear codes duality.
Online Access:	http://ijocta.org/index.php/files/article/view/512

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spelling	doaj-ee0147cf86fa48239ef29b7049e402ce2021-02-17T01:22:55ZengBalikesir UniversityAn International Journal of Optimization and Control: Theories & Applications 2146-09572146-57032017-12-018110.11121/ijocta.01.2018.00512The structure of one weight linear and cyclic codes over Z_{2}^r x (Z_{2} + uZ_{2})^sIsmail Aydogdu0Yildiz Technical University Inspired by the Z2Z4-additive codes, linear codes over Z_{2}^r x (Z_{2} + uZ_{2})^s have been introduced by Aydogdu et al. more recently. Although these family of codes are similar to each other, linear codes over Z_{2}^r x (Z_{2} + uZ_{2})^s have some advantages compared to Z2Z4-additive codes. A code is called constant weight(one weight) if all the codewords have the same weight. It is well known that constant weight or one weight codes have many important applications. In this paper, we study the structure of one weight Z2Z2[u]-linear and cyclic codes. We classify these type of one weight codes and also give some illustrative examples. http://ijocta.org/index.php/files/article/view/512One weight codesZ2Z2[u]-linear codesduality.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Ismail Aydogdu
spellingShingle	Ismail Aydogdu The structure of one weight linear and cyclic codes over Z_{2}^r x (Z_{2} + uZ_{2})^s An International Journal of Optimization and Control: Theories & Applications One weight codes Z2Z2[u]-linear codes duality.
author_facet	Ismail Aydogdu
author_sort	Ismail Aydogdu
title	The structure of one weight linear and cyclic codes over Z_{2}^r x (Z_{2} + uZ_{2})^s
title_short	The structure of one weight linear and cyclic codes over Z_{2}^r x (Z_{2} + uZ_{2})^s
title_full	The structure of one weight linear and cyclic codes over Z_{2}^r x (Z_{2} + uZ_{2})^s
title_fullStr	The structure of one weight linear and cyclic codes over Z_{2}^r x (Z_{2} + uZ_{2})^s
title_full_unstemmed	The structure of one weight linear and cyclic codes over Z_{2}^r x (Z_{2} + uZ_{2})^s
title_sort	structure of one weight linear and cyclic codes over z_{2}^r x (z_{2} + uz_{2})^s
publisher	Balikesir University
series	An International Journal of Optimization and Control: Theories & Applications
issn	2146-0957 2146-5703
publishDate	2017-12-01
description	Inspired by the Z2Z4-additive codes, linear codes over Z_{2}^r x (Z_{2} + uZ_{2})^s have been introduced by Aydogdu et al. more recently. Although these family of codes are similar to each other, linear codes over Z_{2}^r x (Z_{2} + uZ_{2})^s have some advantages compared to Z2Z4-additive codes. A code is called constant weight(one weight) if all the codewords have the same weight. It is well known that constant weight or one weight codes have many important applications. In this paper, we study the structure of one weight Z2Z2[u]-linear and cyclic codes. We classify these type of one weight codes and also give some illustrative examples.
topic	One weight codes Z2Z2[u]-linear codes duality.
url	http://ijocta.org/index.php/files/article/view/512
work_keys_str_mv	AT ismailaydogdu thestructureofoneweightlinearandcycliccodesoverz2rxz2uz2s AT ismailaydogdu structureofoneweightlinearandcycliccodesoverz2rxz2uz2s
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The structure of one weight linear and cyclic codes over Z_{2}^r x (Z_{2} + uZ_{2})^s

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