We consider the Norton algebra associated with a Q -polynomial primitive idempotent of adjacency matrix for distance-regular graph. obtain formula product that we find attractive.

The rank distance was introduced in 1985 by E. Gabidulin [1]. He determined a lower bound for the minimum rank distance of a code. Moreover, he constructed a class of codes which meet this bound: the so-called Gabidulin codes. In this paper, we first characterize the linear isometries for the rank distance. Then we determine the isometry group and the permutation group of Gabidulin codes of ful...

vspace{0.2cm}In this paper, we design a data structure for the following problem. Let $pi$ be an $x$-monotone trajectory with $n$ vertices in the plane and $epsilon >0$. We show how to preprocess $pi$ and $epsilon$ into a data structure such that for any horizontal query segment $Q$ in the plane, one can quickly determine the minimal continuous fraction of $pi$ whose Fr{'e}chet and Hausdo...

In this paper, we describe the properties of the i-components of Hamming codes. We suggest constructions of the admissible families of components of Hamming codes. It is shown that every q-ary code of length m and minimum distance 5 (for q = 3 the minimum distance is 3) can be embedded in a q-ary 1-perfect code of length n = (qm−1)/(q−1). It is also shown that every binary code of length m+k an...

We describe the recent developments concerning the rational analogues of the Beckman-Quarles Theorem, and discuss a related result concerning isometric embeddings in Q of subsets of E. 1 – Let E denote the Euclidean d-space, and let Q denote the Euclidean rational d-space. A mapping f : E → E is called ρ-distance preserving if ‖x − y‖ = ρ implies that ‖f(x)−f(y)‖ = ρ. The Beckman Quarles Theore...

We deal with the minimum distances of q-ary cyclic codes of length qm − 1 generated by products of two distinct minimal polynomials, give a necessary and sufficient condition for the case that the minimum distance is two, show that the minimum distance is at most three if q > 3, and consider also the case q = 3.