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<p>Constant-composition codes (CCCs) are a special type of constant-weight codes which are important in coding theory. In this paper, we use ordered designs OD(3,&#xa0;4,&#xa0;<i>n</i>)s to construct optimal quintuple CCCs of length <i>n</i> with weight four, distance three and the composition [1,&#xa0;1,&#xa0;1,&#xa0;1]. For this purpose, we use ordered candelabra quadruple systems (OCQSs) and pairwise balanced designs to construct OD(3,&#xa0;4,&#xa0;<i>n</i>)s with distance three and present recursive constructions of OCQSs via three wise balanced designs. Consequently, optimal quintuple constant-composition codes with weight four, distance three and the composition [1,&#xa0;1,&#xa0;1,&#xa0;1] are given with some possible exceptions.</p>

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Constructions of quintuple constant-composition codes with weight four and distance three

  • 期刊论文

  • 发表日期：

    2026年5月15日

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  • Lijun Ji,
  • Ming Shi,
  • Zihong Tian,
  • Chaohuan Yang,
  • Jun Zhang

摘要

Constant-composition codes (CCCs) are a special type of constant-weight codes which are important in coding theory. In this paper, we use ordered designs OD(3, 4, n)s to construct optimal quintuple CCCs of length n with weight four, distance three and the composition [1, 1, 1, 1]. For this purpose, we use ordered candelabra quadruple systems (OCQSs) and pairwise balanced designs to construct OD(3, 4, n)s with distance three and present recursive constructions of OCQSs via three wise balanced designs. Consequently, optimal quintuple constant-composition codes with weight four, distance three and the composition [1, 1, 1, 1] are given with some possible exceptions.