Upper and lower bounds on the undetected error probability of binary codes derived from shortened Reed-Solomon codes

Author

Desaki, Yoshihisa ; Fujiwara, Toru ; Kasami, Tadao ; Lin, Shu

Author_Institution

Dept. of Inf. & Comput. Sci., Osaka Univ., Japan

fYear

1992

fDate

16-20 Nov 1992

Firstpage

598

Abstract

The number of codewords with small weights is investigated for the binary codes derived from shortened Reed-Solomon codes. A formula is shown for the exact number of codewords with weight 2 in the binary image of a shortened Reed-Solomon code generated by (X-α). This number does not depend on the choice of the primitive element α. Upper bounds on the number of codewords with small weights are also derived for the binary image of a shortened code generated by (X-α) and (X-1)(X-α) by using the relation between the Reed-Solomon code and Hamming code. The number of codewords with the minimum weight is also discussed for the binary images of other Reed-Solomon codes. By using the results, the undetected error probability is evaluated

Keywords

Reed-Solomon codes; coding errors; probability; Hamming code; binary codes; binary image; lower bounds; shortened Reed-Solomon codes; undetected error probability; upper bounds; weights; Binary codes; Block codes; Circuit testing; Compaction; Error probability; Feedback circuits; Galois fields; Polynomials; Reed-Solomon codes; Upper bound;

fLanguage

English

Publisher

ieee

Conference_Titel

Singapore ICCS/ISITA '92. 'Communications on the Move'

Print_ISBN

0-7803-0803-4

Type

conf

DOI

10.1109/ICCS.1992.254881

Filename

254881