We introduce a new approach which facilitates the calculation of the covering radius of a binary linear code. It is based on determining the normalized covering radius p. For codes of fixed dimension we give upper and lower bounds on p that arc reasonably close. As an application, an explicit formula is given for the covering radius of an arbitrary code of dimension <4. This approach also sheds...

We consider upper bounds on two fundamental parameters of a code; minimum distance and covering radius. New upper bounds on the covering radius of non-binary linear codes are derived by generalizing a method due to S. Litsyn and A. Tiett avv ainen 10] and combining it with a new upper bound on the asymptotic information rate of non-binary codes. The new upper bound on the information rate is an...

Bhandari, M.C. and M.S. Garg, A note on the covering radius of optimum codes, Discrete Applied Mathematics 33 (1991) 3-9. This paper gives a lower bound and an upper bound for the covering radius of optimum codes. The upper bound so obtained is better than other known upper bounds, restricted to optimum codes. Optimum codes of covering radius d1 and d2 are shown to be normal. A binary linear co...

Let Rt,n denote the set of t-resilient Boolean functions of n variables. First, we prove that the covering radius of the binary ReedMuller code RM(2, 6) in the sets Rt,6, t = 0, 1, 2 is 16. Second, we show that the covering radius of the binary Reed-Muller code RM(2, 7) in the set R3,7 is 32. We derive a new lower bound for the covering radius of the Reed-Muller code RM(2, n) in the set Rn−4,n....

In [5], we studied binary codes with covering radius one via their characteristic functions. This gave us an easy way of obtaining congruence properties and of deriving interesting linear inequalities. In this paper we extend this approach to ternary covering codes. We improve on lower bounds for ternary 1-covering codes, the so-called football pool problem, when 3 does not divide n − 1. We als...