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Ars Combinatoria

  • Research article

On the Structure of Optimal Linear Block Codes of Length a Multiple of \(4\) and \(d= 4\)

Morteza Esmaeili1, T.Aaron Gulliver2
1Faculty of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran,
2Department of Electrical and Computer Engineering, University of Victoria, P.O. Box 3055, STN CSC, Victoria, BC, Canada V8W 3P6,
  • Published: 31/01/2005

Abstract

A decomposition of optimal linear block codes with minimum distance \(d = 4\) and length \(4L\) into two subcodes is given such that one of the subcodes is an optimal length \(L\) code with minimum Hamming distance \(4\) and the other is a quasi-cyclic code of index \(4\). It is shown that the \(L\)-section minimal trellis diagram of the code is the product of the minimal trellis diagrams of the subcodes.

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Citation
Morteza Esmaeili, T.Aaron Gulliver. On the Structure of Optimal Linear Block Codes of Length a Multiple of \(4\) and \(d= 4\)[J], Ars Combinatoria, Volume 074. 25-31. .