Covering radius computations for binary cyclic codes
نویسندگان
چکیده
منابع مشابه
On the covering radius of some binary cyclic codes
We compute the covering radius of some families of binary cyclic codes. In particular, we compute the covering radius of cyclic codes with two zeros and minimum distance greater than 3. We compute the covering radius of some binary primitive BCH codes over F2f , where f = 7, 8.
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The results of this paper are concerned with the multi-covering radius, a generalization of covering radius, of Rank Distance (RD) codes. This leads to greater understanding of RD codes and their distance properties. Results on multi-covering radii of RD codes under various constructions are given by varying the parameters. Some bounds are established. A relationship between multi-covering radi...
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An asymmetric binary covering code of length n and radius R is a subset C of the n-cube Qn such that every vector x ∈ Qn can be obtained from some vector c ∈ C by changing at most R 1’s of c to 0’s, where R is as small as possible. K(n,R) is defined as the smallest size of such a code. We show K(n,R) ∈ Θ(2/n) for constant R, using an asymmetric sphere-covering bound and probabilistic methods. W...
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In this two-part paper we introduce the notion of a stable code and give a new upper bound on the normalized covering radius ofa code. The main results are that, for fixed k and large n, the minimal covering radius t[n, k] is realized by a normal code in which all but one of the columns have multiplicity l; hence tin + 2, k] t[n, k] + for sufficiently large n. We also show that codes with n _-<...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1991
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1991-1079013-8