Bursts in m-metric array codes

Fire [P. Fire, A class of multiple-error-correcting binary codes for non-independent errors, Sylvania Reports RSL-E-2, Sylvania Reconnaissance Systems, Mountain View, California, 1959] introduced the concept of bursts for classical codes where codes are subsets/subspaces of the space , the space of all n-tuples with entries from a finite field Fq. In this paper, we introduce the notion of bursts for m-metric array codes where m-metric array codes are subsets/subspaces of the space Matm×s(Fq), the linear space of all m × s matrices with entries from a finite field Fq, endowed with a non-Hamming metric. We also obtain some bounds (analogous to Fire’s bound [P. Fire, A class of multiple-error-correcting binary codes for non-independent errors, Sylvania Reports RSL-E-2, Sylvania Reconnaissance Systems, Mountain View, California, 1959], Rieger’s bound [S.H. Reiger, Codes for the correction of clustered errors, IRE-Trans., IT-6 (1960), 16–21] etc. in classical codes) on the parameters of m-metric array codes for the detection and correction of burst errors.