Self-dual codes over GF(4)

F. J. MacWilliams, A. M. Odlyzko, N. J.A. Sloane, H. N. Ward

Research output: Contribution to journalArticlepeer-review

102 Scopus citations


This paper studies codes C over GF(4) which have even weights and have the same weight distribution as the dual code C. Some of the results are as follows. All such codes satisfy C = C (If C= C, T has a binary basis.) The number of such C's is determined, and those of length ≤14 are completely classified. The weight enumerator of C is characterized and an upper bound obtained on the minimum distance. Necessary and sufficient conditions are given for C to be extended cyclic. Two new 5-designs are constructed. A generator matrix for C can be taken to have the form [I | B], where B = B. We enumerate and classify all circulant matrices B with this property. A number of open problems are listed.

Original languageEnglish (US)
Pages (from-to)288-318
Number of pages31
JournalJournal of Combinatorial Theory, Series A
Issue number3
StatePublished - Nov 1978


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