NDLI: Classification of the Deletion Correcting Capabilities of Reed–Solomon Codes of Dimension <formula><tex>$2$</tex></formula> Over Prime Fields

Content Provider	IEEE Xplore Digital Library
Author	McAven, L. Safavi-Naini, R.
Copyright Year	1963
Abstract	Deletion correction codes have been used for transmission synchronization and, more recently, tracing pirated media. A generalized Reed-Solomon (GRS) code, denoted by GRS_k(l,q,alpha,v), is a code of length l over GF(q) with q^k codewords. These codes have an efficient decoding algorithm and have been widely used for error correction and detection. It was recently demonstrated that GRS codes are also capable of correcting deletions. We consider a subclass of GRS codes with dimension k=2 and q prime, and study them with respect to deletion correcting capability. We give transformations that either preserve the code or maintain its deletion correction capability. We use this to define equivalent codes; and then use exhaustive and selective computer searches to find inequivalent codes with the highest deletion correcting capabilities. We show that, for the class under consideration, up to l-3 deletions may be corrected. We also show that for lles36 there exist codes with q² codewords such that receiving only 3 out of t transmitted symbols of a codeword is enough to recover the codeword, thus meeting the bound specified above. We also specify some "nice" codes which are associated with the smallest field possible for codes of a given length and deletion correcting capability. Some of the identified codes are unique, with respect to the defined equivalence.
Sponsorship	IEEE Information Theory Society
Starting Page	2280
Ending Page	2294
Page Count	15
File Size	929270
File Format	PDF
ISSN	00189448
Volume Number	53
Issue Number	6
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2007-06-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Error correction codes Decoding Information security Computer science Binary codes Propagation losses Internet Software engineering Reed–Solomon Codes deletion correction
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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