A basic theory of two-dimensional cyclic codes (TDC codes) is presented. This theory is applicable to the binary TDC codes of odd area, i.e., the TDC codes with an odd number of symbols from GF(2). It is shown that such TDC codes are completely characterized by the common zeros, which correspond to the roots for ordinary cyclic codes. The fundamental structure of the codes such as the positions...

Various proposals have been made for declustering two-dimensionally tiled data on multiple I/O devices. Recently it has been shown that strictly optimal solutions only exist under very restrictive conditions on the tiling of the two-dimensional space or for very few I/O devices. In this paper we explore allocation methods where no strictly optimal solution exists. We propose a general class of ...

In-plane deformation of foams was studied experimentally by subjecting bidisperse foams to cycles of traction and compression at a prescribed rate. Each foam contained bubbles of two sizes with given area ratio and one of three initial arrangements: sorted perpendicular to the axis of deformation (iso-strain), sorted parallel to the axis of deformation (iso-stress), or randomly mixed. Image ana...

We prove, without assuming the Generalized Riemann Hypothesis, but with at most one exception, that an irreducible cyclic code c(p, m, v) with v prime and p of index 2 modulo v is a two-weight code if and only if it is a semiprimitive code or it is one of the six sporadic known codes. The result is proved without any exception for index-two irreducible cyclic c(p, m, v) codes with v prime not c...

We apply analytical and numerical methods to study the linear stability of stripe patterns in two generalizations of the two-dimensional Swift-Hohenberg equation that include coupling to a mean flow. A projection operator is included in our models to allow exact stripe solutions. In the generalized models, stripes become unstable to the skew-varicose, oscillatory skew-varicose, and cross-roll i...

We introduce circulant matrices that capture the structure of a skew-polynomial ring F[x; θ] modulo the left ideal generated by a polynomial of the type x − a. This allows us to develop an approach to skew-constacyclic codes based on such circulants. Properties of these circulants are derived, and in particular it is shown that the transpose of a certain circulant is a circulant again. This rec...

Let Fq be a finite field with q elements, where q = p , p is a prime, and s is a positive integer. An [n, k, d] linear code C is a k-dimensional subspace of Fq with minimum distance d. It is called cyclic if (c0, c1, . . . , cn−1) ∈ C implies (cn−1, c0, c1, . . . , cn−2) ∈ C. By identifying the vector (c0, c1, . . . , cn−1) ∈ Fq with c0 + c1x+ c2x 2 + · · ·+ cn−1c ∈ Fq[x]/(x − 1), any code C of...