糾兩個(gè)錯(cuò)的二元BCH碼的代數(shù)完全譯碼
AN ALGEBRAIC COMPLETE DECODING OF DOUBLEERROR-CORRECTING BINARY BCH CODES
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摘要: 本文提出糾兩個(gè)錯(cuò)的二元BCH碼的代數(shù)完全譯碼方法。它實(shí)現(xiàn)起來比Hartmann的一步一步譯碼方法速度快,并且當(dāng)對應(yīng)校驗(yàn)子S1、S3的錯(cuò)誤圖樣重量為3時(shí),能找出所有對應(yīng)同樣校驗(yàn)子的重量為3的錯(cuò)誤圖樣。同時(shí),本文也建立了GF(2m)上三次方程在GF(2m)上有三個(gè)不同根的判別式,這在糾三個(gè)錯(cuò)的二元BCH碼的完全譯碼中十分重要。
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關(guān)鍵詞:
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]熊全淹編著,近世代數(shù),上海科學(xué)出版社,1976, p. 132. -
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