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Cosets of Extended BCH Codes of Various Weights


Affiliations
1 PG Department of Mathematics, DAV College, Abohar, India
2 Department of Basic Sciences, Guru Nanak College for Girls, Sri Muktsar Sahib, India
     

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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.
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  • Cosets of Extended BCH Codes of Various Weights

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Authors

Anita Pruthi
PG Department of Mathematics, DAV College, Abohar, India
N. K. Pruthi
Department of Basic Sciences, Guru Nanak College for Girls, Sri Muktsar Sahib, India

Abstract


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.