A minimum distance bound for quasi-nD-cyclic codes

ÖZBUDAK F., Ozkaya B.

FINITE FIELDS AND THEIR APPLICATIONS, vol.41, pp.193-222, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 41
  • Publication Date: 2016
  • Doi Number: 10.1016/j.ffa.2016.06.004
  • Journal Name: FINITE FIELDS AND THEIR APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.193-222
  • Keywords: Quasi-cyclic code, Multidimensional quasi-cyclic code, Multidimensional cyclic code, Trace representation, Multidimensional convolutional code, CONVOLUTIONAL-CODES, ALGEBRAIC STRUCTURE, FINITE-FIELDS, RATE 1/P, CONSTRUCTION
  • Middle East Technical University Affiliated: Yes

Abstract

We provide a new concatenated structure for multidimensional quasi-cyclic (QnDC) codes over F-q and we give a trace representation for their codewords, which extends the known representations of QC and nD cyclic codes. Based on these results, we obtain a minimum distance bound for QnDC dyclic codes. Since QnDC codes are naturally related to nD convolutional codes, this bound also applies to a special class of 1-generator 2D convolutional codes. (C) 2016 Elsevier Inc. All rights reserved.