Showing papers on "GF(2) published in 1981"
TL;DR: This work proposes a method to reduce a set of functions to one polynomial of one variable on GF (2 N ) (extension field overGF (2)), which has remarkable properties based on Frobenius transforms.
Abstract: Every digital information processing is essentially represented by a set n functions of m variables on {0, 1}. We propose a method to reduce such a set of functions to one polynomial of one variable on GF (2 N ) (extension field over GF (2)). Such polynomials have remarkable properties based on Frobenius transforms, which are to serve for effective designs and productions of switching circuits.
3 citations
TL;DR: This correspondence describes a method for achieving synthesis of finite state algorithms by the use of a set of logic elements that execute field operations from the Galois field GF[pn].
Abstract: This correspondence describes a method for achieving synthesis of finite state algorithms by the use of a set of logic elements that execute field operations from the Galois field GF[pn]. The method begins with a definition of the algorithm to be synthesized in a completely specified finite state flow table form. A polynomial expansion of this flow table function is derived. A canonical sequential circuit corresponding to this polynomial expansion is defined. Subsequently, the given algorithm is synthesized using the canonical circuit by specification of a number of arbitrary constants in the canonical circuit. A mechanical method for deriving constants used in the canonical circuits is given. Finally, some estimates on complexity of the given circuit structure are stated assuming the most fundamental logic element structures.
3 citations
1 citations
TL;DR: It is shown that any delayed m-sequence is obtained fast and easily even if the delay is large, and weight 5 primitive polynomials of up to 244 degree are obtained, which are suitable for constructing an m- sequence generator with a simple composition.
1 citations
TL;DR: In this article, the minimal polynomial of a sequence formed by concatenation of two δ-sequences has been derived and the minimal generator of any given sequence of bits can be analytically obtained from the above results.
Abstract: In this paper the minimal polynomial of a sequence formed by concatenation of two δ-sequences has been derived. A further result gives the minimal polynomial of a sequence obtained by concatenation of any sequence V (with known minimal generator) with any of the δ-sequences or its translates. It is shown that the minimal generator of any given sequence of bits can be analytically obtained from the above results.