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

1986-03-04

Malzahn, David H.

Boots, shoes, and leggings

G06F 752

Patent

active

045743614

ABSTRACT:
An apparatus divides one element .alpha..sup.i of a Galois field GF(2.sup.m) by another element .alpha..sup.j of the field. Divider data .alpha..sup.j are supplied to one of the first linear shift registers and to the other first linear shift registers through .alpha..sup.N1, .alpha..sup.N2, . . . multiplier circuits, respectively. Simultaneously, dividend data .alpha..sup.i are supplied to one of the second linear shift registers and to the other second linear shift registers through .alpha..sup.N1, .alpha..sup.N2, . . . multiplier circuits, respectively. "1" detector circuits are connected to the outputs of the first linear shift registers, respectively. The first linear shift registers and the second linear shift registers are shifted several times until any "1" detector circuit detects "1" in response to output signals from a 2-input AND gate. When "1" is detected, a NOR gate supplies a signal of logical "0" to the AND gate, whereby the AND gate stops supplying output signals. 2-input AND circuits are connected at one input terminal to the outputs of the "1" detector circuits and at the other input terminal to the outputs of the second linear shift registers. The AND circuit connected to the "1" detector circuit supplies the data stored in the second linear shift register to which it is connected. The data representing the quotient of the division .alpha..sup.i -.alpha..sup.j, are delivered through an OR circuit.

REFERENCES:
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patent: 4099160 (1978-07-01), Flagg
patent: 4142174 (1979-02-01), Chen
patent: 4473887 (1984-09-01), Odaka
Davida, "Inverse of Elements of a Galois Field", Electronics Letters, vol. 8, No. 21, Oct. 19, 1972, pp. 518-520.
Chien, "Cyclic Decoding Procedures for Bose-Chaudhuri-Hocquenghem Codes", IEEE Trans. on Infor. Theory, vol. IT-10, No. 4, Oct. 1964, pp. 357-363.
Steen, "Error Correction for Voice Grade Data Communication Using a Communication Processor", IEEE Trans. on Communication, vol. COM-22, No. 10, Oct. 1974, pp. 1595-1606.

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