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سند علمی

Self-Dual Codes over GF(4)

F. Jessie MacWilliams, Andrew M. Odlyzko, N. J. A. Sloane, Harold N. Ward

چکیده

This paper studies codes V over GF(4) which have even weights and have the same weight distribution as the dual code FL. Some of the results are as follows. All such codes satisfy VL = 4. (If VI = V, V has a binary basis.) The number of such V's is determined, and those of length <14 are completely classified. The weight enumerator of % is characterized and an upper bound obtained on the minimum distance. Necessary and sufficient conditions are given for %' to be extended cyclic. Two new 5-designs are constructed. A generator matrix for V can be taken to have the form [I 1 B], where BL = B. We enumerate and classify all circulant matrices B with this property. A number of open problems are listed.

اسناد مشابه

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