著者

JAIN Sapna

出版者

九州大学

雑誌

Kyushu Journal of Mathematics (ISSN:13406116)

巻号頁・発行日

vol.62, no.1, pp.189-200, 2008-03

被引用文献数

4

---

An array code/linear array code is a subset/subspace, respectively, of the linear space $ \mathrm{Mat}_{m \chi s} (F_q) $, the space of all $ m \chi s $ matrices with entries froma finite field $ F_q $ endowed with a non-Hamming metric known as the RT-metric or $\rho$-metric or $ m $-metric. In this paper, we obtain a sufficient lower bound on the number of parity check digits required to achieve minimum $\rho$-distance at least $ d $ in linear array codes using an algorithmic approach. The bound has been justified by an example. Using this bound, we also obtain a lower bound on the number$ B_q (m \chi s, d) $ where $ B_q(m \chi s, d) $ is the largest number of code matrices possiblein a linear array code $ V \subseteq \mathrm{Mat}_{m \chi s} (Fq) $ having minimum $\rho$-distance at least $ d $.