Asymptotic Minimum Covering Radius of Block Codes
نویسندگان
چکیده
منابع مشابه
Asymptotic Minimum Covering Radius of Block Codes
In this paper, we restudy the covering radius of block codes from an information theoretic point of view by ignoring the combinatorial formulation of the problem. In the new setting, the formula of the statistically defined minimum covering radius, for which the probability mass of uncovered space by M spheres can be made arbitrarily small, is reduced to a minimization of a statistically define...
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Codes with minimum distance at least d and covering radius at most d− 1 are considered. The minimal cardinality of such codes is investigated. Herewith, their connection to covering problems is applied and a new construction theorem is given. Additionally, a new lower bound for the covering problem is proved. A necessary condition on an existence problem is presented by using a multiple coverin...
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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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The shortest possible length of a q-ary linear code of covering radius R and codimension r is called the length function and is denoted by q(r, R). Constructions of codes with covering radius 3 are here developed, which improve best known upper bounds on q(r, 3). General constructions are given and upper bounds on q(r, 3) for q = 3, 4, 5, 7 and r ≤ 24 are tabulated.
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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 Discrete Mathematics
سال: 2001
ISSN: 0895-4801,1095-7146
DOI: 10.1137/s0895480100379993