Construction of Extremal Type II Codes over ℤ4

Philippe Gaborit, Masaaki Harada

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


In this paper, we give a pseudo-random method to construct extremal Type II codes over ℤ4;. As an application, we give a number of new extremal Type II codes of lengths 24, 32 and 40, constructed from some extremal doubly-even self-dual binary codes. The extremal Type II codes of length 24 have the property that the supports of the codewords of Hamming weight 10 form 5-(24, 10, 36) designs. It is also shown that every extremal doubly-even self-dual binary code of length 32 can be considered as the residual code of an extremal Type II code over ℤ4.

Original languageEnglish
Pages (from-to)257-269
Number of pages13
JournalDesigns, Codes, and Cryptography
Issue number3
Publication statusPublished - 1999


  • Extremal codes and type II codes
  • Self-dual codes over ℤ


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