It is shown that the codewords of binary and ternary Golay codes can be converted into rays in ${\mathbb{RP}}^{23}$ ${\mathbb{RP}}^{11}$ provide proofs Kochen-Specker theorem real state spaces dimensions 24 12, respectively. Some implications these results are discussed.

A problem based on the Extended Euclidean Algorithm applied to a class of polynomials with many factors is presented and believed to be hard. If so, it is a one-way function well suited for applications in digital signatures. Let ) (x P and ) (x Q be polynomials defined over the Integers modulo a prime integer p with ) 1 ( ) ( ) ( 1    p x x Q x P p mod . Also let ) (x A be a polynomial such...

A new decoder is proposed to decode the (23, 12, 7) binary Golay-code up to five errors. It is based on the algorithm that can correct up to four errors for the (24, 12, 8) extended Golay-code proposed by Lin et al., thereby achieving the soft decoding in the real sense for the Golay-code. For a weight-2 or weight-3 error pattern decoded by the hard decoder for correcting up to three errors, on...

In this work we study numbers and polynomials generated by two type of composition of generating functions and get their explicit formulae. Furthermore we state an improvementof the composita formulae's given in [6] and [3], using the new composita formula's we construct a variety of combinatorics identities. This study go alone to dene new family of generalized Bernoulli polynomials which incl...

Sequences with low aperiodic autocorrelation and crosscorrelation are used in communications remote sensing. Golay Shapiro independently devised a recursive construction that produces families of complementary pairs binary sequences. In the simplest case, Rudin–Shapiro sequences, general it what we call Golay–Rudin–Shapiro Calculations by Littlewood show sequences have mean square autocorrelati...

We prove the existence of complexified real arrangements with the same combinatorics but different embeddings in P. Such pair of arrangements has an additional property: they admit conjugated equations on the ring of polynomials over Q( √ 5).

The vertex-edge Wiener polynomials of a simple connected graph are defined based on the distances between vertices and edges of that graph. The first derivative of these polynomials at one are called the vertex-edge Wiener indices. In this paper, we express some basic properties of the first and second vertex-edge Wiener polynomials of simple connected graphs and compare the first and second ve...