In this correspondence, we give lower and upper bounds on the covering radius of codes over the finite ring Z 6 with respect to different distances such as Hamming, Lee, Euclidean and Chinese Euclidean. We also determine the covering radius of various Block Repetition Codes over Z 6.

In this paper, some lower and upper bounds on the covering radius of codes over the nite non chain ring A = F4 + vF4; v2 = v with respect to Bachoc weight is given. Also, the covering radius of various Block Repetition Codes of same and different length over the nite non chain ring A = F4 + vF4; v2 = v is obtained.In this paper, some lower and upper bounds on the covering radius of codes over the nite non chain ring A = F4 + vF4; v2 = v with respect to Bachoc weight is given. Also, the covering radius of various Block Repetition Codes of same and different length over the nite non chain ring A = F4 + vF4; v2 = v is obtained.

In this paper, we have defined ℤq-linear code and constructed some new codes. In particular, we have introduced the concept of ℤq-Simplex codes and proved that it is a [Formula: see text]-linear code for any integer q ≥ 2 and k ≥ 3 where p is the least order element in ℤq. We have given the weight distribution of ℤq-Simplex codes of dimension 2 when q is a prime power and when q is a product of distinct primes.

In this paper, we defined the Z q -linear codes and discussed its various parameters. We constructed Z q -Simplex code and Z q -MacDonald code. For q is prime power, we haveis the Euler f -function. We have given a lower and an upper bounds of its covering radius for q is a prime power.

In this paper, the covering radius of codes over R = Z 2 R * , where R * = Z 2 + vZ 2 , v 2 = v with different weight are discussed. The block repetition codes over R is defined and the covering radius for block repetition codes, simplex code of α-type and β-type in R are obtained.