We analyze 4and 9-linear lifts of the binary [24; 12] and ternary [12; 6]-Golay code under different weight functions on the underlying ring, and present algebraic decoding schemes for these codes.

The concept of weak algebraic hyperstructures or Hv-structures constitutes a generalization of the well-known algebraic hyperstructures (semihypergroup, hypergroup and so on). The overall aim of this paper is to present an introduction to some of the results, methods and ideas about chemical examples of weak algebraic hyperstructures. In this paper after an introduction of basic definitions and...

In general CELP type vocoders provide good speech qu ality around 4.8kbps. Among them, G.723.1 developed f or Internet Phone and videoconferencing includes two v ocoders, 5.3kbps ACELP and 6.3kbps MP-MLQ. Since 6.3kbps MP-MLQ requires large amount of computation for the fixed codebook search, it is difficult to realize r eal time processing for the Internet-based environment. In order to improv...

Error-correcting codes derived from curves in an algebraic geometry are called Algebraic-Geometry Codes. The past couple of decades has seen extraordinary developments in the application of the ideas of algebraic geometry to the construction of codes and their decoding algorithms. This was initiated by the work of Goppa as generalizations of Bose-Chaudhuri-Hocquenghem (BCH), Reed-Solomon (RS), ...

In the auditory system, tonotopy is postulated to be substrate for a place code, where sound frequency encoded by location of neurons that fire during stimulus. Though conceptually simple, computations allow representation intensity and complex sounds are poorly understood. Here, mathematical framework developed in order define clearly conditions support code. To accommodate both information, n...

An interesting class of l inear error-correcting codes has been found by Goppa [3], [4]. This paper presents algebraic decoding algorithms for the Goppa codes. These algorithms are only a little more complex than Berlekamp’s well-known algorithm for BCH codes and, in fact, make essential use of his procedure. Hence the cost of decoding a Goppa code is similar to the cost of decoding a BCH code ...

A new quaternary linear code of length 19, codimension 5, and covering radius 2 is found in a computer search using tabu search, a local search heuristic. Starting from this code, which has some useful partitioning properties, di!erent lengthening constructions are applied to get an in"nite family of new, record-breaking quaternary codes of covering radius 2 and odd codimension. An algebraic co...

Let β be the middle-(1−2β) Cantor set with β ∈ (1/3, 1/2). We give all real numbers t with unique {−1, 0, 1}-code such that the intersections β ∩ ( β + t) are self-similar sets. For a given β ∈ (1/3, 1/2), a criterion is obtained to check whether or not a t ∈ [−1, 1] has the unique {−1, 0, 1}-code from both geometric and algebraic views. Mathematics Subject Classification: 28A80, 28A78

Explaining codon evolution in the standard genetic code is a remarkable subject in Molecular Biology. There are many works which try to develop a model to represent this evolution, sometimes using a certain amount of mathematical tools. The present work has as its main objective to explain one possible dynamical evolution model, which is based in the algebraic approach proposed in 1993 by Horno...

We have designed, implemented, and proved the correctness of a compiler generator that accepts action semantic descriptions of imperative programming languages. The generated compilers emit absolute code for an abstract RISC machine language that currently is assembled into code for the SPARC and the HP Precision Architecture. Our machine language needs no run-time type-checking and is thus mor...