On the Covering Radius of Codes Over Z6

Abstract

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.

Hadamard bent sequences-survey and new results

“…In Table 2 we recall the distribution of matrices per classes of BH(n, q) in the said database. (5,5), BH(6, 3), BH (6,4), BH (6,6), BH (7,6), BH (7,7), BH (8,2), BH (8,8), BH(9, 3), BH (9,6), BH (9,9), BH (9,10), BH (10,4), BH (10,10), BH (11,11), BH (12,2), BH (12,3), BH (12,12), BH (12,36), BH (13,13), BH(13, 60)…”

“…H ∈ BH (6,3), n = 6, q = 3. There are precisely 6+3−1 The above 28 cases satisfy q−1 r=0 y r = 6, but a 2 + b 2 = 6, so BH (6,3) does not contain matrices having eigenvalues of the type of Theorem 6.1. This is confirmed by computation on matrices of BH (6,3).…”

“…There are precisely 6+3−1 The above 28 cases satisfy q−1 r=0 y r = 6, but a 2 + b 2 = 6, so BH (6,3) does not contain matrices having eigenvalues of the type of Theorem 6.1. This is confirmed by computation on matrices of BH (6,3). Remark 6.2.…”

“…While the packing properties of the code with respect to the homogeneous and other metrics have been investigated by various authors [1,13], we focus on the Chinese Euclidean metric and the covering properties in connection with bent sequences. The Chinese Euclidean metric, which is first mentioned in [6], should not be confused with that in [18]. We also associate with every such code of length n a spherical code in dimension 2n.…”