Search results for "Linear code"
showing 9 items of 9 documents
Asymptotically good codes from generalized algebraic-geometry codes
2005
We consider generalized algebraic-geometry codes, based on places of the same degree of a fixed algebraic function field over a finite field. In this note, using a method similar to the Justesen's one, we construct a family of such codes which is asymptotically good.
On the decomposition of prefix codes
2017
Abstract In this paper we focus on the decomposition of rational and maximal prefix codes. We present an effective procedure that allows us to decide whether such a code is decomposable. In this case, the procedure also produces the factors of some of its decompositions. We also give partial results on the problem of deciding whether a rational maximal prefix code decomposes over a finite prefix code.
Design of efficient codes for the AWGN channel based on decomposable binary lattices
1998
This work is concerned with the use of binary decomposable lattice codes over the QAM Gaussian channel. First, we investigate the structure of such class of lattices: we derive consistency conditions for the binary codes appearing in their decomposition and express their nominal coding gain and some bounds for their error coefficient in terms of the parameters of the component codes. Then we describe a general multistage bounded‐distance decoding algorithm with low complexity and we evaluate its performance. Finally, we develop a design example and report the corresponding simulation results; as a reference some comparisons with standard TCM codes are also presented.
New lower bounds for the minimum distance of generalized algebraic geometry codes
2013
Abstract In this paper, we give a new lower bound for generalized algebraic geometry codes with which we are able to construct some new linear codes having better parameters compared with the ones known in the literature. Moreover, we give a relationship between a family of generalized algebraic geometry codes and algebraic geometry codes. Finally, we propose a decoding algorithm for such a family.
MMD codes in a more general sense
2002
Summary form only given. The author deals with the characterisation of maximum minimum distance (MMD) codes in a more general sense, which has been completed in a joint work with Olsson. As in the m=1 case the weight distribution of an MMD code /spl Cscr/ is uniquely determined by its parameters [n,k,d]/sub q/.
On the size of transducers for bidirectional decoding of prefix codes
2012
In a previous paper [L. Giambruno and S. Mantaci, Theoret. Comput. Sci. 411 (2010) 1785–1792] a bideterministic transducer is defined for the bidirectional deciphering of words by the method introduced by Girod [ IEEE Commun. Lett. 3 (1999) 245–247]. Such a method is defined using prefix codes. Moreover a coding method, inspired by the Girod’s one, is introduced, and a transducer that allows both right-to-left and left-to-right decoding by this method is defined. It is proved also that this transducer is minimal. Here we consider the number of states of such a transducer, related to some features of the considered prefix code X . We find some bounds of such a number of states in relation wi…
Steiner systems and configurations of points
2020
AbstractThe aim of this paper is to make a connection between design theory and algebraic geometry/commutative algebra. In particular, given any Steiner SystemS(t, n, v) we associate two ideals, in a suitable polynomial ring, defining a Steiner configuration of points and its Complement. We focus on the latter, studying its homological invariants, such as Hilbert Function and Betti numbers. We also study symbolic and regular powers associated to the ideal defining a Complement of a Steiner configuration of points, finding its Waldschmidt constant, regularity, bounds on its resurgence and asymptotic resurgence. We also compute the parameters of linear codes associated to any Steiner configur…
Diagonal space time hadamard codes with erasure decoding algorithm
2005
A major challenge in the area of space time (ST) codes is to find codes suitable for efficient decoding, thus overcoming the problem of many existing ST code designs which require maximum-likelihood (ML) decoding. A solution could be to apply single-input single-output (SISO) channel codes and theory over temporal channel fading to the multi-input single-output (MISO) code construction and classical suboptimum decoding methods. For these purposes, an ST code construction which allows the use of efficient decoding algorithms is described. We propose a concatenated code, where the inner code is the diagonal ST Hadamard (D-STH) code with Paley constructions and the outer code is an algebraic b…
Recursive modeling for completed code generation
2009
Model-Driven Development is promising to software development because it can reduce the complexity and cost of developing large software systems. The basic idea is the use of different kinds of models during the software development process, transformations between them, and automatic code generation at the end of the development. But unlike the structural parts, fully-automated code generation from the behavior parts is still hard, if it works at all, restricted to specific application areas using a domain specific language, DSL.This paper proposes an approach to model the behavior parts of a system and to embed them into the structural models. The underlying idea is recursive refinements …