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On the Nonexistence of Quaternary [51, 4, 37] Codes

✍ Scribed by I. Landgev; T. Maruta; R. Hill

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 258 KB
Volume: 2
Category: Article
ISSN: 1071-5797
DOI: 10.1006/ffta.1996.0007

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✦ Synopsis

In this paper we prove the nonexistence of quaternary linear codes with parameters [51,4, 37]. This result gives the exact value of n q (k, d) for q ϭ 4, k ϭ 4, d ϭ 37 and 38. These were the only minimum distances for which the optimal length of a four-dimensional quaternary code was unknown. The proof is geometrical and relies heavily on results about the structure of certain sets of points in PG(2, 4).

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