A covering problem over finite rings

✍ Scribed by I.N. Nakaoka; O.J.N.T.N. dos Santos

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 467 KB
• Volume: 23
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/j.aml.2009.09.022

✦ Synopsis

Given a finite commutative ring with identity A, define c(A, n, R) as the minimum cardinality of a subset H of A n which satisfies the following property: every element in A n differs in at most R coordinates from a multiple of an element in H. In this work, we determine the numbers c(Z m , n, 0) for all integers m ≥ 2 and n ≥ 1. We also prove the relation c(S × A, n, 1) ≤ c(S, n -1, 0)c(A, n, 1), where S = F q or Z q and q is a prime power. As an application, an upper bound is obtained for c(Z m p , n, 1), where p is a prime.