纠两个错的二元BCH码的代数完全译码
AN ALGEBRAIC COMPLETE DECODING OF DOUBLEERROR-CORRECTING BINARY BCH CODES
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摘要: 本文提出纠两个错的二元BCH码的代数完全译码方法。它实现起来比Hartmann的一步一步译码方法速度快,并且当对应校验子S1、S3的错误图样重量为3时,能找出所有对应同样校验子的重量为3的错误图样。同时,本文也建立了GF(2m)上三次方程在GF(2m)上有三个不同根的判别式,这在纠三个错的二元BCH码的完全译码中十分重要。
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Abstract: An algebraic complete decoding of double-error-correcting binary BCH codes is shown in this paper. It is faster than Hartmann s decoding of double-errcr-correcting binary BCH eodes of primitive length. And when the weight of the error pattern corresponding with synlromes S1 and S3 is equal to 3, this deeoding can find all error patterns of weigth 3 with the same syndromes. On the other hand, a discrimination of judging whether or not a cubie equation over GF(2m) has three distinct roots in GF(2m) is also shown in this paper. It is very improtant in the complete decoding of triple-error-correcting binary BCH codes. -
D. C. Govenstein, W. W. Peterson and N. Zierler, Inform. Contr. 3(1960), 291.[3]C. R. P. Hartmann, IEEE Trans. on IT, IT-17(1971), 765.[4]J. A. V. D. Horst and T. Berger, IEEE Trans.on IT, IT-22(1976), 138.[5]熊全淹编著,近世代数,上海科学出版社,1976, p. 132. -
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