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On extremal additive \({\mathbb{F}}_4\) codes of length 10 to 18. (English) Zbl 1007.94027

The minimum weight of an even trace-self-dual additive code of length \(n\) over \(F_4\) is at most \(2[n/6]+2\); codes meeting this bound are called extremal. The enumeration of such codes is pushed here to \(n=10\), where the class number is found to be 19. Under the hypothesis that at least two minimal words have the same support, also length 14 is treated and for length 18 such a code turns out to be equivalent to the extremal linear hermitian-self-dual code.

MSC:

94B60 Other types of codes
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
94B65 Bounds on codes

Software:

Magma

References:

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