Abstract
Decoding errors can be seen from the point of view of the receiver or the transmitter. This naturally leads to different functions for the decoding error probability. We study their behaviour and the relation between these two functions. Though both functions are equally good when used to compare two codes with respect to decoding errors only one of them reflects in general the properties such a function should have. This is not the function one usually considers in the literature when studying decoding errors. Both functions coincide only if the underlying code is perfect. The investigations in this paper can be seen as a continuation of earlier work of MacWilliams (see chap. 16.1 in [2]).
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References
Baicheva T, Bouyukliev I, Dodunekov S, Willems W (2005) Teaching linear codes. Matematica Balkanika, New Series, Vol. 19, Fasc. 1–2, 3–16
Berlekamp ER (1984) Algebraic coding theory. Revised 1984 edition, Aegean Park Press
Bouyukliev I (2004) On the binary projective codes with dimension 6. Bulgarian Academy of Sciences, Preprint No 1/2004, Sofia
Bouyukliev I, Bouyuklieva S, Gulliver TA, Östergård PRJ, Classification of optimal binary self- orthogonal codes. To appear in AAECC
Faldum A, Trustworthiness of error-correcting codes. To appear
F-W Fu T Kløve VK-W Wei (2003) ArticleTitleOn the undetected error probability for binary codes IEEE Trans Inform Theory 49 IssueID2 382–390 Occurrence Handle1063.94125 Occurrence Handle1966786 Occurrence Handle10.1109/TIT.2002.807299
T Helleseth T Kløve V Levenshtein (2004) ArticleTitleThe simplex codes and even weight binary codes for error correction IEEE Trans Inform heory 50 2818–2823 Occurrence Handle10.1109/TIT.2004.836708
Helleseth T, Kløve T, Levenshtein V (2004) Error-correction capability of binary linear codes and the discrete simplex problem. Preprint version
Kløve T, Korzhik V (1995) Error detecting codes: general theory and their application in feedback communication systems. Kluwer Academic Publishers
G Poltyrev (1994) ArticleTitleBounds on the decoding error probability of binary linear codes via their spectra IEEE Trans Inform Theory 40 1284–1292 Occurrence Handle0821.94035 Occurrence Handle1301434 Occurrence Handle10.1109/18.335935
W Willems (1999) Codierungstheorie DeGruyter Berlin
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Communicated by T. Helleseth.
J. Lafuente and G. Ochoa are supported by MTM2004-08219-C02-01.
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Faldum, A., Lafuente, J., Ochoa, G. et al. Error Probabilities for Bounded Distance Decoding. Des Codes Crypt 40, 237–252 (2006). https://doi.org/10.1007/s10623-006-0010-x
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DOI: https://doi.org/10.1007/s10623-006-0010-x