T HIS INTRODUCTORY section applies to general binary rate k/n convolutional codes. In Section II we specialize to rate one-half to describe a class of codes that allows an interesting mod ification of the stack decoding algorithm [l]-[2]. Section III presents our simulation results. Let G be a conventional convolutional encoder [3] whose rows are the first k rows of a polynomial n X n matrix B ...

We simplify the proofs of four results in [3], restating two of them for greater clarity. The main purpose of this note is to give a brief transparent proof of Theorem 7 of [3], the main upper bound of that paper. The secondary purpose is to give a more direct statement and proof of the integer programming determination of covering radius of [3]. Theorem 7 of [3] follows from a simple result in...

Process algebras extended by a concept to present timing behaviour have been very recently proposed as a good modelling tool for the combined analysis of qualitative and quantitative system behaviour. We introduce a a process algebra including exponentially distributed time delays and a systematic approach to compute the underlying labelled transition system and continuous time Markov process. ...

..........................................................................................................................................1 1. Background................................................................................................................................1 2. The Upper Triangular Lattice Form (utlt) of B ....................................................................

We show how the theory of affine geometries over the ring Z/〈q−1〉 can be used to understand the properties of toric and generalized toric codes over Fq. The minimum distance of these codes is strongly tied to the collections of lines in the finite geometry that contain subsets of the exponent vectors of the monomials that are evaluated to produce the standard generator matrix for the code. We a...

We considered repeated-root cyclic codes whose block length is divisible by the characteristic of the underlying field. Cyclic self dual codes are also the repeated root cyclic codes. It is known about the one-level squaring construction for binary repeated root cyclic codes. In this correspondence, we introduced of two level squaring construction for binary repeated root cyclic codes of length...

We present multi-point algebraic geometric codes overstepping the Gilbert-Varshamov bound. The construction is based on the generalized Hermitian curve introduced by A. Bassa, P. Beelen, A. Garcia, and H. Stichtenoth. These codes are described in detail by constrcting a generator matrix. It turns out that these codes have nice properties similar to those of Hermitian codes. It is shown that the...

We propose a secret sharing scheme based on rings or modules that admit a decomposition given by orthogonal idempotents of the ring. The secret is decomposed into partial secrets that belong to the projections induced by every idempotent. These projections are indeed ideal codes and thus the subsecrets are distributed among a group of users using the generator matrix of these ideal codes.

A class of one-dimensional convolutional codes will be presented. They are all MDS codes, i. e., have the largest distance among all one-dimensional codes of the same length n and overall constraint length δ. Furthermore, their extended row distances are computed, and they increase with slope n − δ. In certain cases of the algebraic parameters, we will also derive parity check matrices of Vande...

We consider codes defined over an affine algebra A = R[X1, . . . , Xr]/ 〈t1(X1), . . . , tr(Xr)〉, where ti(Xi) is a monic univariate polynomial over a finite commutative chain ring R. Namely, we study the A−submodules of A (l ∈ N). These codes generalize both the codes over finite quotients of polynomial rings and the multivariable codes over finite chain rings. Some codes over Frobenius local ...