In this paper from q-ary perfect codes new completely regular q-ary codes are constructed. In particular, two new ternary completely regular codes are obtained from ternary Golay [11, 6, 5] code. The first [11, 5, 6] code with covering radius ρ = 4 coincides with the dual Golay code and its intersection array is (22, 20, 18, 2, 1; 1, 2, 9, 20, 22) . The second [10, 5, 5] code, with covering rad...

We prove a new sufficient condition for a Boolean function to be extremal balanced or maximally nonlinear, in odd or even dimension. Under this condition, we deduce the balanced covering radius ρB(n) and the covering radius ρ(n). We prove some general properties about maximally nonlinear or extremal balanced functions. Finally, an application to even weights Boolean functions is given.

In this paper we determine an upper bound for the covering radius of a q-ary MacDonald codeCk;u(q). Values of nq(4; d), the minimal length of a 4-dimensional q-ary code with minimum distance d is obtained for d = q 1 and q 2. These are used to determine the covering radius of C3;1(q),C3;2(q) and C4;2(q).

A new family of binary linear completely transitive (and, therefore, completely regular) codes is constructed. The covering radius of these codes is growing with the length of the code. In particular, for any integer ρ ≥ 2, there exist two codes with d = 3, covering radius ρ and length ( 4 ρ 2 )

The length function lq(r,R) is the smallest length of a q-ary linear code of covering radius R and codimension r. New upper bounds on lq(r, 2) are obtained for odd r ≥ 3. In particular, using the one-to-one correspondence between linear codes of covering radius 2 and saturating sets in the projective planes over finite fields, we prove that

The Newton radius of a code is the largest weight of a uniquely correctable error. The covering radius is the largest distance between a vector and the closest codeword. A couple of relations involving the Newton and covering radii are discussed. c © 2001 Elsevier Science B.V. All rights reserved.

Monitoring the long-distance pipelines, rivers, roads and boundary lines with wireless sensor networks belongs to one-dimensional region monitoring. This paper primarily studies the coverage problems of the sensor networks in one-dimensional regions. Firstly, the onedimensional random coverage model is processed for the sensor nodes in one-dimensional monitoring region, and a formula is given t...

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.