Optimal Codes for Correcting a Single (Wrap-Around) Burst of Erasures

In 2007, Martinian and Trott presented codes for correcting a burst of erasures with a minimum decoding delay. Their construction employs [n,k] codes that can correct any burst of erasures (including wrap-around bursts) of length n-k . They raised the question if such [n,k] codes exist for all integ...

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Bibliographic Details
Published in:IEEE transactions on information theory 2008-09, Vol.54 (9), p.4361-4364
Main Authors: Hollmann, Henk D. L., Tolhuizen, Ludo M. G. M.
Format: Article
Language:English
Subjects:
Applied sciences
Binary system
Burst
Bursting
Codes
Coding, codes
Construction
Decoding
Delay
erasures
Exact sciences and technology
Galois fields
Information theory
Information, signal and communications theory
Integers
Legged locomotion
Linear code
linear codes
Numbers
Optimization
Recursive
Signal and communications theory
Telecommunications and information theory
Terminology
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Summary:In 2007, Martinian and Trott presented codes for correcting a burst of erasures with a minimum decoding delay. Their construction employs [n,k] codes that can correct any burst of erasures (including wrap-around bursts) of length n-k . They raised the question if such [n,k] codes exist for all integers k and n with 1\leq k\leq n and all fields (in particular, for the binary field). In this correspondence, we answer this question affirmatively by giving two recursive constructions and a direct one.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2008.928287