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Computer Programming: A Class of Triple Error Correcting BCH Codes

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In a recent paper, Bracken and Helleseth [2009] showed that one can construct triple-error-correcting codes using zero set consisting different zero set than the BCH codes. In this correspondence we present some new triple error correcting code having zeros and where gcd (2k, n) =1 and n be odd. Keywords: Triple error, Parity Check matrix & minimum distance. 1 Introduction BCH codes [R.Bose and D.Ray-Chaudari, 1960] are of great practical importance for error-correction, particularly if the expected errors are small compared with the length. The BCH code is a subset of cyclic code. The binary primitive triple –error-correcting BCH code with minimum distance d = 7 is a cyclic code. We consider a finite field with elements. g(x) be the generator polynomial of triple –error-correcting BCH code having be its Zeros. The set is known as triple. Kasami showed that one can construct similar triple-error-correcting codes using zeros sets of different triples. Later Helleseth and Bracken presented some new triples and in addition they gave some new method for finding these triple. In this paper with the help of some new zeros we construct some triple-error-correcting BCH like codes. Let H = be the parity check Matrix of the triple error correcting BCH code where the order of the matrix is 3n by . The code C = [ , , d]is a code of dimension and minimum distance d= 7 between any pair of codewords.Generally we are interested in finding triples s.t. H is the parity
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