Starting from a linear [n, k, d]q code with dual distance d ⊥, we may construct an [n−d⊥, k−d⊥+1,≥ d]q code with dual distance at least l d⊥ q m using construction Y1. The inverse construction gives a rule for the classification of all [n, k, d]q codes with dual distance d ⊥ by adding d⊥ further columns to the parity check matrices of the smaller codes. Isomorph rejection is applied to guarante...

There is a type of distance-regular graph, said to be $Q$-polynomial. In this paper we investigate generalized $Q$-polynomial property involving graph that not necessarily distance-regular. We give detailed description an example associated with the projective geometry $L_N(q)$.

The Wiener index of a graph Gis defined as W(G) =1/2[Sum(d(i,j)] over all pair of elements of V(G), where V (G) is the set of vertices of G and d(i, j) is the distance between vertices i and j. In this paper, we give an algorithm by GAP program that can be compute the Wiener index for any graph also we compute the Wiener index of HAC5C7[p, q] and HAC5C6C7[p, q] nanotubes by this program.

The exact sizes of optimal q-ary codes of length n, constant weightw and distance d = 2w− 1 have only been determined for q ∈ {2, 3}, and for w|(q − 1)n and n sufficiently large. We completely determine the exact size of optimal q-ary codes of constant weight three and minimum distance five for all q by establishing a connection with Hanani triple packings, and settling their existence.