Lahtonen, _I., An optimal polynomial for a covering radius problem, Discrete Mathematics 105 (1992) 313-317. A. Tietlvlinen discovered, how polynomials with suitable Fourier-Krawtchouk coefficients can be used to get information about the covering radius of a code as a function of the dual distance. In this note we determine the optimal polynomials satisfying Tietavlinen’s conditions. This give...

Weanalyse a probabilistic argument that gives a semi-random construction for a permutation code on n symbols with distance n− s and size (s!(log n)1/2), and a bound on the covering radius for sets of permutations in terms of a certain frequency parameter.

Tietäväinen’s upper and lower bounds assert that for block-length-n linear codes with dual distance d, the covering radius R is at most n2 − ( 2 − o(1)) √ dn and typically at least n2 − Θ( √ dn log nd ). The gap between those bounds on R − n2 is an Θ( √ log nd ) factor related to the gap between the worst covering radius given d and the sphere-covering bound. Our focus in this paper is on the c...

New lower bounds on the minimum length of terror correcting BCH codes with covering radius at most 2t are derived.

The covering radius problem has been considered by many authors (e.g. [ 1, 5, 61). Finally, let t(n, k) be the minimum possible covering radius for an (n, k) code and k(n, p) the minimum possible dimension of a code with covering radius p. The study of t(n, k) was initiated by Karpovsky. For a survey of these questions, see ]41. The main goal of this paper is to find good linear coverings. The ...

The paper addresses the problem of locating sensors with a circular field of view so that a given line segment is under full surveillance, which is termed as the Disc Covering Problem on a Line. The cost of each sensor includes a fixed component f , and a variable component b that is proportional to the field-of-view area. When only one type of sensor or, in general, one type of disc, is availa...

A number of upper and lower bounds are obtained for K( n, R), the minimal number of codewords in any binary code of length n and covering radius R. Several new constructions are used to derive the upper bounds, including an amalgamated direct sum construction for nonlinear codes. This construction works best when applied to normal codes, and we give some new and stronger conditions which imply ...

Let N ≥ 2 and let 1 < a1 < · · · < aN be relatively prime integers. Frobenius number of this N-tuple is defined to be the largest positive integer that cannot be expressed as P N i=1 aixi where x1, ..., xN are non-negative integers. The condition that gcd(a1 , ..., aN ) = 1 implies that such number exists. The general problem of determining the Frobenius number given N and a1, ..., aN is NP-har...

We give an explicit upper bound of the minimal number of balls of radius 1/2 which form a covering of a ball of radius T > 1/2 in R, n > 2.