Results 271 to 280 of about 51,101 (296)
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On the covering radius of subcodes of a code
IEEE Transactions on Information Theory, 1991Summary: Let \(C\) be a binary linear code with covering radius \(R\), and \(C_ 0\) a subcode of \(C\) of codimension \(i\). An upper bound is obtained for the covering radius of \(C_ 0\) in terms of \(R\) and \(i\). When \(C_ 0=\{0\}\), the bound becomes the sphere covering bound for \(R\).
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On a bound involving the covering radius and the Newton radius
Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252), 2002An error e is (uniquely) correctable if and only if it is the unique coset leader in its coset. The study of unique coset leaders is therefore important when one wants to study decoding beyond half the minimum distance. The covering radius is the largest weight of a coset leader. The author examines a binary linear code. They show a nontrivial relation
E. Gabidulin, T. Klove
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A note on covering radius of MacDonald codes
Proceedings ITCC 2003. International Conference on Information Technology: Coding and Computing, 2004We determine an upper bound for the covering radius of a q-ary MacDonald code C/sub k,u/(q). Values of n/sub q/(4, d), the minimal length of a 4-dimensional q-ary code with minimum distance d is obtained for d = q/sup 2/ - 1 and q/sup 2/ - 2. These are used to determine the covering radius of C/sub 3,1/(q), C/sub 3,2/(q) and C/sub 4,2/(q).
Mahesh C. Bhandari, C. Durairajan 0001
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Explicit codes with low covering radius
IEEE Transactions on Information Theory, 1988A series of explicit low-rate binary linear codes which have relatively low covering radius and can be rapidly decoded is exhibited. These codes can be derived from higher dimensional analogues of the Gale-Berlekamp switching game. Conjectures of independent interest involving Hadamard matrices are given, which would yield semi-explicit covering codes ...
János Pach, Joel Spencer
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Covering radius and writing on memories
1991We investigate and survey some connections between coding theory and the problem of writing on binary memories subject to constraints on transitions between states. More precisely, the existence of good covering codes is used for two purposes: computing the capacity (maximum achievable rate) for some special classes of translation-invariant ...
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Covering radius: Improving on the sphere-covering bound
1989Currently, the best general lower bound for the covering radius of a code is the sphere covering bound. For binary linear codes, the paper presents a new method to detect cases in which this bound is not attained.
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The complexity of computing the covering radius of a code
IEEE Transactions on Information Theory, 1984The problem of finding the covering radius of a binary linear code is shown to be nondeterministic polynomial (NP)-hard. In fact, a problem that is complete for the class \(\Pi^ p_ 2\) in the polynomial hierarchy is shown to be reducible to the covering-radius problem, so that finding the covering radius is strictly harder than any NP-complete problem ...
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Packing Radius vs Covering Radius
Proceedings. IEEE International Symposium on Information Theory, 2005P. Sole, P. Stokes
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An improved upper bound on covering radius
1986A simple upper bound on covering radius yields new information on various codes. It leads us to show that the nonlinear codes of Sloane and Whitehead [18] are quasi-perfect. We get some new bounds for the Berlekamp-Gale switching problem [7]. It gives the exact covering radius for some codes of length up to 31 and is within 1 or 2 of the exact value ...
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