Codes and invariant theory
نویسندگان
چکیده
منابع مشابه
Codes and invariant theory
There is a beautiful analogy between most of the notions for lattices and codes and it seems to be quite promising to develop coding theory analogues of concepts known in the theory of lattices and modular forms and vice versa. Some of these analogies are presented in this short note that intends to survey recent developments connected to my talk Hecke-Operators for codes in Luminy, on May 9, 2...
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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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Let cq(n,R) denote the minimum cardinality of a subset H in Fq such that every word in this space differs in at most R coordinates from a multiple of a vector in H , where q is a prime power. In order to explore the symmetries of such coverings, a few algebraic properties of invariant sets under certain translation are investigated. As an application, a new class of upper bounds on cq(n,R) is r...
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ژورنال
عنوان ژورنال: Mathematische Nachrichten
سال: 2004
ISSN: 0025-584X,1522-2616
DOI: 10.1002/mana.200310204