Completely reducible super-simple designs with block size five and index two

Hengjia Wei, Hui Zhang, Gennian Ge

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

Complete reducible super-simple (CRSS) designs are closely related to $$q$$q-ary constant weight codes. A (v,k,λ)-CRSS design is just an optimal (v,2(k-1),k)λ+1 code. In this paper, we mainly investigate the existence of a (v,5,2)-CRSS design and show that such a design exists if and only if v≡1,5 (mod20) and v ≥21, except possibly when v = 25. Using this result, we determine the maximum size of an (n,8,5)3 code for all n≡ 0,1,4,5 (mod20) with the only length n=25 unsettled.

Original languageEnglish
Pages (from-to)589-600
Number of pages12
JournalDesigns, Codes, and Cryptography
Volume76
Issue number3
DOIs
StatePublished - 6 Sep 2015
Externally publishedYes

Keywords

  • Completely reducible super-simple designs
  • Constant weight codes
  • Group divisible designs
  • Super-simple designs

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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