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Ars Combinatoria

  • Research article

Classification of Optimal Linear \(\mathbb{Z}_4\) Rate \(1/2\) Codes of Length \(\leq 8 \)

T.Aaron Gulliver1, John N.C.Wong1
1Department of Electrical and Computer Engineering, University of Victoria, P.O. Box 3055, STN CSC, Victoria, BC, Canada V8W 3P6,
  • Published: 31/10/2007

Abstract

In this paper, we classify all optimal linear \([n, n/2]\) codes over \(\mathbb{Z}_4\) up to length \(n = 8\), and determine the number of optimal codes which are self-dual and formally self-dual. Optimal codes with linear binary images are identified. In particular, we show that for length \(8\), there are nine optimal codes for the Hamming distance, one optimal code for the Lee distance, and two optimal codes for the Euclidean distance.

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Citation
T.Aaron Gulliver, John N.C.Wong. Classification of Optimal Linear \(\mathbb{Z}_4\) Rate \(1/2\) Codes of Length \(\leq 8 \)[J], Ars Combinatoria, Volume 085. 287-306. .