In this paper we present an algorithmic approach to the problem of the divisibility of the number of solutions to a system of polynomial equations. Using this method we prove that all binary cyclic codes with two zeros over F2fand minimum distance 5 are quasi-perfect for f les 10. We also present elementary proofs of divisibility results that, in some cases, improve previous results

In this correspondence, we correct an error in the correspondence cited in the title.

Introduces a generalization of the concepts of coverings and packings in Hamming space called weighted coverings and packings. This allows to formulate a number of well-known coding theoretical problems in a uniform manner. The authors study the existence of perfect weighted codes, discuss connections between weighted coverings and packings, and present many constructions for them.

All known results on covering radius are presented, as well as some new results. There are a number of upper and lower bounds, including asymptotic results, a few exact determinations of covering radius, some extensive relations with other aspects of coding theory through the Reed-Muller codes, and new results on the least covering radius of any linear[n,k]code. There is also a recent result on the complexity of computing the covering radius.

A new upper bound on the covering radius of binary linear codes improves on previously known bounds for some codes. The bound is[W/2]+\rho_{2}, whereWis one of the weights occurring among the codewords, and\rho_{2}is the covering radius of an associated code. Some comparisons with other bounds are made.

Three applications of a theorem of I. J. Good are made: a simplification of the fast Hadamard transform algorithm of R.R. Green used in the decoding of first-order Reed-Muller codes, a simple proof of the well-known Parseval formula, and an application to the discrete one-dimensional Fourier transform.

The coseta + Aof the linear codeAhas weight distribution related to that ofA^{\perp}and ofA^{\perp} \cap a^{\perp}.

The coset leader of greatest weight in the 3-error-correcting BCH code of length2^{m}-1has weight 5, for oddm \geq 5.