Abstract
We define additive self-dual codes over G F ( 4 ) with minimal shadow, and we prove the nonexistence of extremal Type I additive self-dual codes over G F ( 4 ) with minimal shadow for some parameters.
Highlights
There are many interesting classes of codes in coding theory such as cyclic codes, quadratic residue codes, algebraic geometry codes, and self-dual codes
We prove the nonexistence of extremal Type I codes with minimal shadow for some parameters
We investigate Type I additive self-dual codes over GF (4)
Summary
There are many interesting classes of codes in coding theory such as cyclic codes, quadratic residue codes, algebraic geometry codes, and self-dual codes. If the code length is large, determining the highest minimum weight of self-dual codes becomes difficult. Conway and Sloane gave an upper bound on the minimum weight of binary self-dual codes [2]. They used the concept of shadow codes. Bouyuklieva and Willems studied binary self-dual codes for which the minimum weight of the shadow codes had the smallest possible value. They proved that extremal binary self-dual codes with minimal shadow for particular parameters do not exist [4].
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