Let $n_q(k,d)$ denote the smallest value of $n$ for which there exists a linear $[n,k,d]$-code over the Galois field $GF(q)$. An $[n,k,d]$-code whose length is equal to $n_q(k,d)$ is called {em optimal}. In this paper we present some matrix generators for the family of optimal $[n,3,d]$ codes over $GF(7)$ and $GF(11)$. Most of our given codes in $GF(7)$ are non-isomorphic with the codes pre...

Combinatorial codes, i.e. subsets of the power set, naturally arise as the language of neural networks in the brain and silicon. A number of combinatorial codes in the brain arise as a pattern of intersections of convex sets in a Euclidean space. Such codes are called convex. Not every code is convex. What makes a code convex and what determines its embedding dimension is still poorly understoo...

This paper concerns the maximum-likelihood channel estimation for MIMO systems with orthogonal space-time block codes when the finite alphabet constraint of the signal constellation is relaxed. We study the estimation subspace for the channel coefficients that this approach generates. We provide an algebraic characterisation of this subspace which turns the optimization problem into a purely al...

Vision is a sense that humans and most animals rely the most onto. Although this sense seems pretty trivial, the visual stimulus is composed of many different dimensions which makes it very complex to decompose, analyze and understand. Scientists state that roughly half of our brain is used for vision processing, it is therefore a very interesting and intriguing area for researchers as it can p...

A table of binary constant weight codes of length n <; 28 is presented. Explicit constructions are given for most of the 600 codes in the table; the majority of these codes are new. The known techniques for constructing constant weight codes are surveyed, and also a table is given of (unrestricted) binary codes of length J1 <; 28.

We study the asymptotic behavior of solutions of one coupled PDE-ODE system arising in mathematical biology as a model for the development of a forest ecosystem. In the case where the ODE-component of the system is monotone, we establish the existence of a smooth global attractor of finite Hausdorff and fractal dimension. The case of the non-monotone ODE-component is much more complicated. In p...

Compared with classical block codes, efficient list decoding of rank-metric codes seems more difficult. The evidences to support this view include: (i) so far people have not found polynomial time list decoding algorithms of rank-metric codes with decoding radius beyond (1 − R)/2 (where R is the rate of code) if ratio of the number of rows over the number of columns is constant, but not very sm...

This paper investigated the moisture absorption, mechanical behavior and the dielectric performance of hybrid and non-hybrid polymeric composites. Hand lay-up technique was used for processing carbon; glass reinforced polyester resin composites (non-hybrid) and carbon-glass/polyester hybrid composites with various fiber configurations. The maximum resistance of water absorption was obtained for...

We consider optimal constant weight codes over arbitrary alphabets. Some of these codes are derived from good codes over the same alphabet, and some of these codes are derived from block design. Generalizations of Steiner systems play an important role in this context. We give several construction methods for these generalizations. An interesting class of codes are those which form generalized ...

Neural codes are collections of binary strings motivated by patterns of neural activity. In this paper, we study algorithmic and enumerative aspects of convex neural codes in dimension 1 (i.e. on a line or a circle). We use the theory of consecutive-ones matrices to obtain some structural and algorithmic results; we use generating functions to obtain enumerative results.