Hamming Distance of Constacyclic Codes of Length ps Over F pm +uF pm +u²F pm
Open Access
- 4 October 2021
- journal article
- research article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Access
- Vol. 9, 141064-141078
Abstract
Let $p$ be any prime, $s$ and $m$ be positive integers. In this paper, we completely determine the Hamming distance of all constacyclic codes of length $p^s$ over the finite commutative chain ring $\mathbb {F}_{p^m}+ u\mathbb {F}_{p^m} + u^{2}\mathbb {F}_{p^m}\,\,\, (u^3=0)$ . As applications, we identify all maximum distance saparable codes (i.e., optimal codes with respect to the Singleton bound) among them.Keywords
Funding Information
- Centre of Excellence in Econometrics, Faculty of Economics, Chiang Mai University, Chiang Mai, Thailand
- Research Administration Centre, Chiang Mai University
This publication has 27 references indexed in Scilit:
- Constacyclic codes of length overJournal of Algebra, 2010
- Self-dual codes over commutative Frobenius ringsFinite Fields and Their Applications, 2010
- Constacyclic Codes of Length $2^s$ Over Galois Extension Rings of ${\BBF}_{2}+u{\BBF}_2$IEEE Transactions on Information Theory, 2009
- On (1−u) -cyclic codes overApplied Mathematics Letters, 2008
- On the linear ordering of some classes of negacyclic and cyclic codes and their distance distributionsFinite Fields and Their Applications, 2008
- Cyclic and Negacyclic Codes Over Finite Chain RingsIEEE Transactions on Information Theory, 2004
- New linear codes over F/sub 5/ obtained by tripling method and improvements on boundsIEEE Transactions on Information Theory, 2002
- On the Hamming distance of linear codes over a finite chain ringIEEE Transactions on Information Theory, 2000
- Type II codes over F/sub 2/+uF/sub 2/IEEE Transactions on Information Theory, 1999
- Applications of Coding Theory to the Construction of Modular LatticesJournal of Combinatorial Theory, Series A, 1997