DOUBLE ERROR CORRECTING CODES WITH IMPROVED CODE RATES

Martin Rakús - Peter Farkaš

   In [1] a new family of error detection codes called Weighted Sum Codes were proposed. In [2] it was noted that these codes are equivalent to lengthened Reed Solomon Codes, and shortened versions of lengthened Reed Solomon codes, respectively, constructed over GF(2^(h/2)). It was also shown that it is possible to use these codes for correction of one error in each codeword over GF(2^(h/2)). In [3] a class of modified Generalized Weighted Sum Codes for single error and conditionally double error correction were presented. In this paper we present a new family of double error - correcting codes with code distance d_m=5. The weight spectrum for [59,49,5] code constructed over GF(8) which is an example of the new codes was obtained by computer using its dual [4]. The code rates of the new codes are higher than the code rate of ordinary Reed Solomon codes constructed over the same finite fields.

Keywords: linear block code, finite field, Reed Solomon codes, code rate, code distance, error control code

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