A symmetric Roos bound for linear codes

Journal of Combinatorial Theory. Series A

Volumn 113, Issue 8, 2006, Pages 1677-1688

  Duursma, Iwan M ^a   Pellikaan, Ruud ^b  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Cyclic code; Dual BCH code; Minimum distance bound; Roos bound

Indexed keywords

EID: 33748420796     PISSN: 00973165     EISSN: 10960899     Source Type: Journal    
DOI: 10.1016/j.jcta.2006.03.020     Document Type: Article

References (21)

1. Bose R.C., and Ray-Chaudhuri D.K. On a class of error-correcting binary group codes. Inform. Control 3 (March 1960) 68-79
2. Bose R.C., and Ray-Chaudhuri D.K. Further results on error-correcting binary group codes. Inform. Control 3 (September 1960) 279-290
3. Brouwer A.E. Bounds on the minimum distance of linear codes. http://homepages.cwi.nl/htbin/aeb/lincodbd
4. I.M. Duursma, Decoding linear codes, preprint CNRS UPR-9016, Luminy, France, 1994
5. Duursma I.M., and Kötter R. Error-locating pairs for cyclic codes. IEEE Trans. Inform. Theory IT-40 (1994) 1108-1121
6. Duursma I.M. Monomial embeddings of the Klein curve. in: G. Faina (Guest-Ed.). Discrete Math. 208/209 (1999) 235-246
7. Feng G.-L., and Tzeng K.K. A generalization of the Berlekamp-Massey algorithm for multisequence shift-register synthesis with applications to decoding cyclic codes. IEEE Trans. Inform. Theory IT-37 (September 1991) 1274-1287
8. Feng G.-L., and Tzeng K.K. Decoding cyclic and BCH codes up to actual minimum distance using nonrecurrent syndrome dependence relations. IEEE Trans. Inform. Theory IT-37 (November 1991) 1716-1723
9. Feng G.-L., and Tzeng K.K. A new procedure for decoding cyclic and BCH codes up to actual minimum distance. IEEE Trans. Inform. Theory IT-40 (September 1994) 1364-1374
10. Hartmann C.R.P., and Tzeng K.K. Generalizations on the BCH bound. Inform. Control 20 (1972) 489-498
11. Hocquenghem A. Codes correcteurs d'erreurs. Chiffres 2 (September 1959) 147-156
12. R. Kötter, An unified description of an error locating procedure for linear codes, in: Proc. Int. Workshop Algebraic Combinator. Coding Theory, Voneshta Voda, Bulgaria, 1992
13. van Lint J.H., and Wilson R.M. On the minimum distance of cyclic codes. IEEE Trans. Inform. Theory IT-32 (1986) 23-40
14. R. Pellikaan, On decoding linear codes by error correcting pairs, preprint, Eindhoven University of Technol., 1988
15. Pellikaan R. On decoding by error location and dependent sets of error positions. Discrete Math. 106-107 (1992) 369-381
16. Pellikaan R. On the existence of error-correcting pairs. J. Statist. Plann. Inference 51 (1996) 229-242
17. Pellikaan R. The shift bound for cyclic, Reed-Muller and geometric Goppa codes. In: Pellikaan R., Perret M., and Vlǎduţ S.G. (Eds). Arithmetic, Geometry and Coding Theory 4. Luminy, 1993 (1996), de Gruyter, Berlin 155-174
18. Roos C. A generalization of the BCH bound for cyclic codes, including the Hartmann-Tzeng bound. J. Combin. Theory Ser. A 33 (1982) 229-232
19. Roos C. A new lower bound for the minimum distance of a cyclic code. IEEE Trans. Inform. Theory IT-29 (1983) 330-332
20. Shen B.-Z., and Tzeng K.K. A code decomposition approach for decoding cyclic and algebraic-geometric codes. IEEE Trans. Inform. Theory 41 (November 1995) 1969-1987
21. Shen K.K., Wang C., Tzeng K.K., and Shen B.-Z. Generation of matrices for determining minimum distance and decoding of cyclic codes. IEEE Trans. Inform. Theory 42 (March 1996) 653-657