On the covering radius of some modular codes

Abstract

This paper gives lower and upper bounds on the covering radius of codes over Z 2 s with respect to homogenous distance. We also determine the covering radius of various Repetition codes, Simplex codes (Type α and Type β) and their dual and give bounds on the covering radii for MacDonald codes of both types over Z 4 .

On ℤq-linear and ℤq-Simplex codes and its related parameters forqis a prime power

“…Every k dimension Z q -linear code with length n and minimum distance d is called [n, k, d] Z q -linear code. A matrix whose rows are the basis elements of a Z q -linear code C is called a generator matrix of C. There are many researchers doing research on code over finite rings [4], [9], [10], [11], [13], [14], [18]. In the last decade, there are many researchers doing research on codes over Z 4 [1], [2], [3], [8], [15].…”

“…The covering radius of Simplex codes and MacDonald codes over finite field and finite rings were discussed in [12], [14]. …”

On the Covering Radius of Codes over Z p k

“…What started with the ring Z 4 , was later generalized to the rings Z 2 s , Z 2 + uZ 2 , Z 4 + uZ 4 , F p + uF p etc. [5][6][7][8]. Covering Radius is a widely discussed parameter for the codes with respect to the Hamming weight [9].…”

“…The Covering Radius for the codes with respect to the Lee distance was first investigated for the ring Z 4 by Aoki [11]. Later, working on the Covering Radius of codes the with respect to the Lee distance gained interest [6,12,13]. We are particulary interested to find the Covering Radius for Repetition Codes, Since the Covering Radius of the Repetition Codes simplifies the process of finding the Covering Radius for many existing codes.…”

On the Covering Radius of Codes Over Z4 with Chinesh Euclidean Weight

“…In 1999, Sole et al gave many upper and lower bounds on the covering radius of a code over Z 4 with chinese euclidean distances. In [12], the covering radius of some particular codes over Z 4 have been investigated. In this correspondence, we consider the ring Z 4 .…”