On the covering radius of Z/sub 4/-codes and their lattices

Lexicodes over rings

“…The right side of (2) is obtained from the redundancy bound [1,Theorem 4.6]. Since each vector in Z n 4 has distance δ − 1 or less to some vector in C n , the covering radius of C n is at most δ − 1.…”

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

“…In particular, for q = 4, R(S k+1 ) ≤ 5 4 3 29 18 1 . k k + + − for k ≥ 2 because of simple calculation R(S 2 ) = 3.…”

“…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].…”

An algorithm for maximising covered area

“…A large body of literature on this topic has concentrated on packing spheres of identical size in Euclidean space (Kershner 1939;Krieger and Schaffner 1971;Honig 1993;Convay and Sloane 1998;Graham and Lubachevsky 1998;Zeger 1997a,b, 2002;Aoki and Gaborit 1999;Zong 1999;Hsiang 2001;Bajic and Woods 2003;Szpiro 2003). The packing methods involve constructing high dimensional lattices, which serve as centres for spheres.…”