In this paper, we consider the minimum Hamming weight for linear codes over special finite quasi-Frobenius rings. Furthermore, we obtain minimal free $R$-submodules of a finite quasi-Frobenius ring $R$  which contain a linear code and derive the relation between their minimum Hamming weights. Finally, we suggest an algorithm that computes this weight using the Grobner basis and we show that und...

Hamming graphs are Cartesian products of complete graphs and partial Hamming graphs are their isometric subgraphs. The Hamming polynomial h(G) of a graph G is introduced as the Hamming subgraphs counting polynomial. Kk-derivates ∂kG (k ≥ 2) of a partial Hamming graph are also introduced. It is proved that for a partial Hamming graph G, ∂h(G) ∂xk = h(∂kG). A couple of combinatorial identities in...

A weighted Hamming metric is introduced in [4] and it showed that the binary generalized Goppa code is a perfect code in some weighted Hamming metric. In this paper, we study the weight structures which admit the binary Hamming code and the extended binary Hamming code to be perfect codes in the weighted Hamming metric. And, we also give some structures of a 2-perfect code and how to construct ...

The Hamming weight of the non-adjacent form is studied in relation to the Hamming weight of the standard binary expansion. In particular, we investigate the expected Hamming weight of the NAF of a n-digit binary expansion with k ones where k is either fixed or proportional to n. The expected Hamming weight of NAFs of binary expansions with large (≥ n/2) Hamming weight is studied. Finally, the c...

The Hamming weight of the non-adjacent form is studied in relation to the Hamming weight of the standard binary expansion. In particular, we investigate the expected Hamming weight of the NAF of a n-digit binary expansion with k ones where k is either fixed or proportional to n. The expected Hamming weight of NAFs of binary expansions with large (≥ n/2) Hamming weight is studied. Finally, the c...

Abstract A maximal partial Hamming packing of Zn 2 is defined by us to be a family S of mutually disjoint translates of Hamming codes of length n, such that any translate of any Hamming code of length n intersects at least one of the translates of Hamming codes in S. The number of translates of Hamming codes in S is the packing number, and a partial Hamming packing is strictly partial if the fa...

This paper contains a new algorithm that recognizes whether a given graph G is a Hamming graph , i . e . a Cartesian product of complete graphs , in O ( m ) time and O ( n 2 ) space . Here m and n denote the numbers of edges and vertices of G , respectively . Previously this was only possible in O ( m log n ) time . Moreover , we present a survey of other recognition algorithms for Hamming grap...