منابع مشابه
Intersection of Isomorphic Linear Codes
Given an (n, k) linear code C over GF(q), the intersection of C with a code ?(C), where ? # Sn , is an (n, k1) code, where max[0, 2k&n] k1 k. The intersection problem is to determine which integers in this range are attainable for a given code C. We show that, depending on the structure of the generator matrix of the code, some of the values in this range are attainable. As a consequence we giv...
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We study isomorphic properties of two generalizations of intersection bodies the class I k of k-intersection bodies in R and the class BPk of generalized k-intersection bodies in R. In particular, we show that all convex bodies can be in a certain sense approximated by intersection bodies, namely, if K is any symmetric convex body in R and 1 6 k 6 n− 1 then the outer volume ratio distance from ...
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In this paper we construct evaluation codes on zero-dimensional complete intersections in toric varieties and give lower bounds for their minimum distance. This generalizes the results of Gold–Little–Schenck and Ballico–Fontanari who considered evaluation codes on complete intersections in the projective space.
متن کاملComputation of Minimum Hamming Weight for Linear Codes
In this paper, we consider the minimum Hamming weight for linear codes over special finite quasi-Frobenius rings. Furthermore, we obtain minimal free $R$-submodules of a finite quasi-Frobenius ring $R$ which contain a linear code and derive the relation between their minimum Hamming weights. Finally, we suggest an algorithm that computes this weight using the Grobner basis and we show that und...
متن کاملAn intersection problem for codes
Let [s]” denote all sequences a’ = (a,, . . , a,) of integers with 1 <xi 2 S. Consider a subset A of [s]“. It is called (t,, . . , &)-intersecting if for any two members ci, b E A and any 1 s i < s there are at least r, positions j, where both a’ and b have entry i, that is, a, = b, = i. The problem of determining max IAl for A being (t,, . . . , t,)-intersecting is considered. In particular, t...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1997
ISSN: 0097-3165
DOI: 10.1006/jcta.1997.2805