ON THE COVERING RADIUS OF SOME CODES OVER R = Z2 + uZ2, WHERE u2 = 0

In the last decade, there are many researchers doing research on code over finite rings. In particular, codes over Z4, Z2 + uZ2 where u2 = 0 received much attention [1, 2, 3, 4, 5, 9, 11, 12, 14, 16, 17]. The covering radius of binary linear codes were studied [6, 7]. Recently the covering radius of codes over Z4 has been investigated with respect to Lee and Euclidean distances [1, 15]. In 1999, Sole et al gave many upper and lower bounds on the covering radius of a code over Z4 with different distances. In the recent paper [15], the covering radius of some particular codes over Z4 have been investigated. In this correspondence, we consider the ring R = Z2 + uZ2 where u2 = 0. In this paper, we investigate the covering radius of the Simplex codes (both types) and their duals, MacDonald codes and repetition codes over R. We also generalized some of the known bounds in [1]. A linear code C of length n over R is an additive subgroup of Rn. An element of C is called a codeword of C and a generator matrix of C is a matrix whose rows generate C. The Hamming weight wH(x) of a vector x in Rn is the number of non-zero components. The Lee weight for a codeword x = (x1, x2,. . . , xn) is defined by