جستجوی مقالات مرتبط با کلیدواژه « codes » در نشریات گروه « ریاضی »

We collect together some known results concerning the codes from adjacency matrices of the graph with vertices the nodes of the m-ary n-cube $Q^m_n$ and with adjacency defined by the Lee metric, and include some new results.

In this paper, we use an irreducible plane-cubic curves in the projective plane $PG(2,q)$ to construct (k,3)-arcs of size $4nu$ where $lceil frac{q+1-2sqrt{q}}{4}rceilleqnuleqlfloor frac{q+1+2sqrt{q}}{4} rfloor$. Each of these arcs gives rise to an error-correcting code that corrects the maximum possible number of errors for its length. Furthermore, we discuss the completeness of each arc. The isotropy subgroup of each arc are determined. All Griesmer codes that correspond to plane-cubic curves are given for $7leq qleq 37,q$ is a prime.

For q in {7,8,9,11,13,16}, we consider the primitive actions of L2(q) and use Key-Moori Method 1 as described in [5, 6] to construct designs from the orbits of the point stabilisers and from any union of these orbits. We also use Key-Moori Method 2 (see [8]) to determine the designs from the maximal subgroups and the conjugacy classes of elements of these groups. The incidence matrices of these designs are then used to generate associated binary codes. The full automorphisms of these designs and codes are also determined.