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Algebraic Structures of Constacyclic Codes Over Finite Chain Rings and Power Series Rings

  • M. Beygi
  • S. NamaziEmail author
  • H. Sharif
Research Paper
  • 3 Downloads
Part of the following topical collections:
  1. Mathematics

Abstract

Let R be a chain ring with the maximal ideal \(\langle \gamma \rangle\). In this paper, we shall study \((r_1+r_2\gamma )\)-constacyclic codes of arbitrary length over R, where \(r_1, r_2\) are units in R. We shall obtain the generators of these codes and their duals. Moreover, a minimal spanning set (and so a generator matrix) for a constacyclic code is obtained. We shall determine the minimum Hamming distance of a constacyclic code over the chain ring R. At last, we shall study some constacyclic codes over formal power series rings. The minimal spanning set for these codes are also established.

Keywords

Linear code Constacyclic code Finite chain ring Formal power series ring Minimum Hamming distance 

Mathematics Subject Classification

94B05 94A55 94B15 58F15 58F17 

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Copyright information

© Shiraz University 2019

Authors and Affiliations

  1. 1.Department of Mathematics, College of SciencesShiraz UniversityShirazIran

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