On the Covering Radius Problem for Codes II. Codes of Low Dimension; Normal and Abnormal Codes
نویسندگان
چکیده
منابع مشابه
On the covering radius of codes
Designing a good error-correcting code is a packing problem. The corresponding covering problem has received much less attention: now the codewords must be placed so that no vector of the space is very far from the nearest codeword. The two problems are quite different, and with a few exceptions good packings, i.e. codes with a large minimal distance, are usually not especially good coverings. ...
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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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It is proved that codes of length n, covering radius Z?, and minimum Hamming distance 2R-1 are normal if R does not divide n. Constructions for abnormal codes with covering radius R and minimum Hamming distance at least R-l are given.
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In network code setting, a constant dimension code is a set of k-dimensional subspaces of F nq . If F_q n is a nondegenerated symlectic vector space with bilinear form f, an isotropic subspace U of F n q is a subspace that for all x, y ∈ U, f(x, y) = 0. We introduce isotropic subspace codes simply as a set of isotropic subspaces and show how the isotropic property use in decoding process, then...
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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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ژورنال
عنوان ژورنال: SIAM Journal on Algebraic Discrete Methods
سال: 1987
ISSN: 0196-5212,2168-345X
DOI: 10.1137/0608050