โ Scribed by S. Al-Bassam; R. Venkatesan; B. Bose
No coin nor oath required. For personal study only.
An (m) error at bit i causes bits i,i + 1,..., and i+ m -1 (or up to the end of the word) to be in error, inflicting m consecutive errors. The most practical cases are when m --2 which is referred to as adjacent errors and when m --n (the length of the word) in which an error causes the rest of the bit stream to be complemented (or in error). An (m) t-ec/d-ed code denotes a code which is able to correct any t (m) errors and detect arty d (m) errors.
In this paper, a new distance measure (similar to the Hamming distance) is defined from which the necessary and sufficient conditions for (m) t-ec/d-ed codes are obtained. To design such codes, a simple trArmformation between the t-ec/d-ed and (m) t-ec/d-ed codes is introduced and a one-to-one map is established. The advantage of this map is two-fold. Firstly, all the well-known t-ee/d-ed codes can be used as (m) codes and secondly the well-developed encod~r/decoder clrcuita for the t-ec/d-ed codes along with a few xoa gates can be used to realize the (m) t-ec/d-ed codes.
๐ SIMILAR VOLUMES
Saidi S., Codes for perfectly correcting errors of limited size, Discrete Mathematics 118 (1993) 207-223. In this paper we study an analogue of perfect codes: codes that perfectly correct errors of limited size, assuming that there is a bound on the number of these errors. Stein's (m, n) crosses (