Apparatus for dividing the elements of a Galois field

Details Apparatus for dividing the elements of a Galois field Apparatus for dividing the elements of a Galois field

1983-03-10

1986-01-28

Malzahn, David H.

Boots, shoes, and leggings

364765, G06F 752

Patent

active

045675686

ABSTRACT:
Data representing one element .alpha..sup.i of a Galois field GF(2.sup.m) are stored in a first linear shift register, and data representing another element .alpha..sup.j of the Galois field GF(2.sup.m) are stored in a second linear shift register. 2.sup.m elements of Galois field GF(2.sup.m) are divided into n groups. A table of the reciprocals of n elements located at specific positions respectively in n groups is stored in a converter which includes a decoder and an encoder. The data representing element .alpha..sup.j are supplied from the second linear shift register to the decoder. If the data representing the reciprocal of element .alpha..sup.j are stored in the converter, they are read from the encoder. If they are not stored in the converter, the first linear shift register and the second linear shift register are shifted N times by control pulses generated by a NOR gate and an AND gate until any one of the reciprocal data are read from the encoder, whereby the register supplies data representing .alpha..sup.i+N and the register supplies data representing .alpha..sup.- (j+N). A multiplier multiplies element .alpha..sup.i by reciprocal .alpha..sup.j or multiplies element .alpha..sup.i+N by reciprocal .alpha..sup.-(j+N), thereby performing the division: a.sup.i .div..alpha..sup.j (=.alpha..sup.i-j).

REFERENCES:
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patent: 4142174 (1979-02-01), Chen
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patent: 4473887 (1984-09-01), Odaka
Michelson, "Computer Implementation of Decoders for Several BCH Codes" Proceedings of the Symposium on Computer Processing in Communications, New York, Apr. 8-10, 1969, Polytechnik Press, Brooklyn, pp. 401-414.
Justesen, "On the Complexity of Decoding Reed-Solomon Codes" IEEE Tran. on Infor. Theory, vol. IT-22 No. 2, Mar. 1976, pp. 237-238.
Chen, "Multisequence Linear Shift Reg. Synthesis & Its Application to BCH Decoding" IEEE Trans. on Communication, vol. COM-24, No. 4, Apr. 1976 pp. 438-440.

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