MacWilliams identities for m-spotty weight enumerators of codes over rings.
Anuradha Sharma, Amit Kumar Sharma · Australas. J Comb. · 2014
Computer memory systems using high-density RAM chips are vulnerable to m-spotty byte errors when they are exposed to high-energy particles. These errors can be effectively detected or corrected using (m-spotty) byte error-control codes. In order to study the properties of these codes and to measure their error-detection and error-correction performance, m-spotty weight enumerators are introduced and studied. In this paper, we extend notions of m-spotty weight enumerator, split m-spotty weight enumerator, r-fold joint m-spotty weight enumerator, complete m-spotty weight enumerator and byte-weight enumerator (with respect to both mspotty Hamming and m-spotty Lee metrics) for byte error-control codes over the finite chain ring Fq + uFq + u Fq + · · ·+ ue−1Fq (u = 0) or the ring Fq+uFq+vFq+uvFq (u 2 = 0, v = 0, uv = vu), where Fq is the finite field of order q. We also discuss some of their applications and establish MacWilliams identities for each of the above-mentioned enumerators.