On self-dual affine-invariant codes
نویسندگان
چکیده
منابع مشابه
On Self-Dual Affine-Invariant Codes
An extended cyclic code of length 2 m over GF(2) cannot be self-dual for even m. For odd m, the Reed-Muller code [2 m, 2 m1, 2(m + 1)/2] is affine-invariant and selfdual, and it is the only such code for m = 3 or 5. We describe the set of binary self-dual affine-invariant codes of length 2 m for m = 7 and m = 9. For each odd m, m >i 9, we exhibit a self-dual affine-invariant code of length 2 m ...
متن کاملSelf-dual codes and invariant theory
Abstract. A formal notion of a Typ T of a self-dual linear code over a finite left Rmodule V is introduced which allows to give explicit generators of a finite complex matrix group, the associated Clifford-Weil group C(T ) ≤ GL|V |(C), such that the complete weight enumerators of self-dual isotropic codes of Type T span the ring of invariants of C(T ). This generalizes Gleason’s 1970 theorem to...
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An affine invariant point on the class of convex bodies Kn in R, endowed with the Hausdorff metric, is a continuous map from Kn to R which is invariant under one-to-one affine transformations A on R, that is, p ` A(K) ́ = A ` p(K) ́ . We define here the new notion of dual affine point q of an affine invariant point p by the formula q(K) = p(K) for every K ∈ Kn, where K denotes the polar of K with...
متن کاملGroup code structures on affine-invariant codes
A group code structure of a linear code is a description of the code as one-sided or two-sided ideal of a group algebra of a finite group. In these realizations, the group algebra is identified with the ambient space, and the group elements with the coordinates of the ambient space. It is well known that every affine-invariant code of length pm, with p prime, can be realized as an ideal of the ...
متن کاملOn self-dual MRD codes
We determine the automorphism group of Gabidulin codes of full length and characterise when these codes are equivalent to self-dual codes.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1994
ISSN: 0097-3165
DOI: 10.1016/0097-3165(94)90014-0