@article{9daf7dc6b0d345c5b5c882104ca05977,
title = "Redundant residue polynomial codes",
abstract = "In this paper, a new class of error-correcting linear block codes using symbols from GF(2m) is presented. These codes are not cyclic codes, but posses instead a unique algebraic structure. It is shown that they are instantaneously decodable with a modest amount of hardware consisting almost entirely of mod 2 adders for correcting burst errors. Furthermore, their efficiency compares favorably with the Varsharmov-Gilbert bound for both random errors over GF(2m) and burst errors over GF(2).",
author = "Bossen, {D. C.} and Yau, {S. S.}",
note = "Funding Information: In this paper we will introduce a class of error-correcting linear block codes, called redundant residue polynomial codes. The codes use symbols from GF(2m). It is anticipated that these codes may be useful in binary systems, where errors are most likely to occur within certain blocks, as for example, in the memory system of a digital computer. If each symbol from GF(2 m) is coded as a binary m-tuple, these codes can be used as a burst-error correcting code for the transmission of binary information. The most powerful existing class of codes with symbols from GF(2 m) are those discovered by Bose and Ray-Chaudhuri (1960). The efficiency of the redundant residue polynomial codes is as good as many of these. The redundant residue polynomial codes require 2t check symbols for each t symbols to be corrected. The efficiency of these codes is found to always lie above the Varsharmov-Gilbert bound for codes with symbols from GF(2~). The important existing classes of codes for burst-error correction consist of the cyclic codes of Fire (1959) and of Reed and Solomon (1960). Stone (1963) and Mandelbaum (1968) have also considered a * The work reported here was supported in part by the U. S. Air Force Office of Scientific l~esearch under Grant No. AF-AFOSR-1292-67. t D. C. Bossen is now with IBM Corporation. Poughkeepsie, New York. 597 class of codes suitable for burst-error correction. Cyclic codes require a relatively small amount of hardware for encoding and decoding, but a number of units of time are required for the decoding process.",
year = "1968",
month = dec,
doi = "10.1016/S0019-9958(68)91025-5",
language = "English (US)",
volume = "13",
pages = "597--618",
journal = "Information and Control",
issn = "0019-9958",
publisher = "Elsevier Inc.",
number = "6",
}