Uniform i-Spotty-byte Error Control Codes

Abstract

Irregular-spotty-byte error control codes were devised by the author in [2] and their properties were further studied in [3] and [4]. These codes are suitable for semi-conductor memories where an I/O word is divided into irregular bytes not necessarily of the same length. The $i$-spotty-byte errors are defined as $t_i$ or fewer bit errors in an $i$-byte of length $n_i$, where $1\le t_i\le n_i$ and $1\le i\le s$. However, an important and practical situation is when $i$-spotty-byte errors caused by the hit of high energetic particles are confined to $i$-bytes of the same size only which are aligned together or in words errors occur usually in adjacent RAM chips at a particular time. Keeping this view, in this paper, we propose a new model of $i$-spotty-byte errors, viz. uniform $i$-spotty-byte errors and present a new class of codes, viz. uniform $i$-spotty-byte error control codes which are capable of correcting all uniform $i$-spotty-byte errors of $i$-spotty measure $\mu$ (or less). The study made in this paper will be helpful in designing modified semi-conductor memories consisting of irregular RAM chips with those of equal length aligned together.