Cosets of Extended BCH Codes of Various Weights
Anita Pruthi1, N.K.Pruthi2
1PG Department of Mathematics, DAV College, Abohar,
2Department of Basic Sciences, Guru Nanak College for Girls, Sri Muktsar Sahib,
*Corresponding Author E-mail:maths.anita@gmail.com, knavneet.pu@gmail.com
1 INTRODUCTION:
To control transmission errors in a data communication system, one can use a code in three ways: purely for error detection, purely for error correction, or for a combination of error correction and detection. Error correcting codes have been widely studied in these decades, e.g. see McWilliam and Sloane [1977]. The family of triple-error-correcting binary BCH codes of length n=2m-1 has been thoroughly studied since 1960’s. The weight distribution of these codes was determined by Kasami [1971] for odd m. For even m, method of Kasami didn’t work. Berlekamp [1967, 1978] gave the weight distribution of extended codes for even values of m.
In 1970’s the covering radius of these code were shown in a series of papers by Assmus and Mattson [1976], Horst and Berger [1976] and Hellseth [1978] to be r=5. Coset distribution of these codes were given by Charpin et. al..
4. REFERENCES:
MacWilliams, F.J. and Sloane, N.J.A [1977]: “The Theory of Error-Correcting Codes,” North Holland, Amsterdam, pp. 288.
Kasami, T. [1971] “The weight enuerators for several classes of subcodes of the second order binary Reed-Muller codes.” Inf. Contr., vol. 18, pp. 369- 394.
Berlekamp, E., McEliece, R. and Tilborg, H. V. [1978]: “On the inherent intractability of certain coding problems." IEEE Transaction on Information Theory, vol. 24, pp. 384-386.
Berlekamp, Elwyn R. [1967]: “Nonbinary BCH decoding”, International Symposium on Information Theory, San Remo, Italy.
Assmus, E. F., Mattson, H. F.[1976]: “Some 3-error-correcting BCH codes have covering radius 5.” IEEE Trans. Information. Theory., 22, p. 348–349.
Horst, J.A. van der and Berger, T. [1976]: “Complete decoding of triple-error-correcting binary BCH codes.” IEEE Trans. Info. Th. 22, p. 138–147.
Helleseth, T. [1978]: “All binary 3-error-correcting BCH codes of length 2m−1 have covering radius 5.” IEEE Trans. Info. Th. 24, p. 257–258.
Received on 16.01.2014 Accepted on 31.01.2014 © EnggResearch.net All Right Reserved Int. J. Tech. 4(1): Jan.-June. 2014; Page 57-61 |