Certain binary asymmetric channels, such as Zchannels in which one of the two crossover probabilities is zero, demand optimal ones densities different from 50%. Some broadcast channels, such as broadcast binary symmetric channels (BBSC) where each component channel is a binary symmetric channel, also require a non-uniform input distribution due to the superposition coding scheme, which is known...

We study the linear codes and their extensions associated with sets of points in the plane corresponding to cubic curves. Instead of merely studying linear extensions, all possible extensions of the code are studied. In this way several new results are obtained and some existing results are strengthened. This type of analysis was carried out by Alderson, Bruen, and Silverman [J. Combin. Theory ...

We prove the existence and uniqueness of solutions of a class of weakly non-linear wave equations in a semi-infinite region 0 ≤ x, t < L/ √ | | under arbitrary initial and boundary conditions. We also establish the asymptotic validity of formal perturbation approximations of the solutions in this region.

The interplay between coding theory and t-designs started many years ago. While every t-design yields a linear code over every finite field, the largest t for which an infinite family of t-designs is derived directly from a linear or nonlinear code is t = 3. Sporadic 4-designs and 5-designs were derived from some linear codes of certain parameters. The major objective of this paper is to constr...

The concept of parity check matrices of linear binary codes has been extended by Heden [9] to parity check systems of nonlinear binary codes. In the present paper we extend this concept to parity check systems of nonlinear codes over finite commutative Frobenius rings. Using parity check systems, results on how to get some fundamental properties of the codes are given. Moreover, parity check sy...

A binary nonlinear code can be represented as a union of cosets of a binary linear subcode. In this paper, the complexity of some algorithms to obtain this representation is analyzed. Moreover, some properties and constructions of new codes from given ones in terms of this representation are described. Algorithms to compute the minimum distance of binary nonlinear codes, based on known algorith...

Complete (n, r)-arcs in PG(k − 1, q) and projective (n, k, n − r)q-codes that admit no projective extensions are equivalent objects. We show that projective codes of reasonable length admit only projective extensions. Thus, we are able to prove the maximality of many known linear codes. At the same time our results sharply limit the possibilities for constructing long nonlinear codes. We also s...

We show that if a linear code admits an extension, then it necessarily admits a linear extension. There are many linear codes that are known to admit no linear extensions. Our result implies that these codes are in fact maximal. We are able to characterize maximal linear (n, k, d)q-codes as complete (weighted) (n, n − d)-arcs in PG(k−1, q). At the same time our results sharply limit the possibi...

A classic result of Delsarte connects the strength (as orthogonal array) of a linear code with the minimum weight of its dual: the former is one less than the latter. Since the paper of Hammons et al., there is a lot of interest in codes over rings, especially in codes over Z4 and their (usually non-linear) binary Gray map images. We show that Delsarte’s observation extends to codes over arbitr...