In this Macaulay2 \cite{M2} package we define an object called {\it linear code}. We implement functions that compute basic parameters and objects associated with a code, such as generator parity check matrices, the dual length, dimension, minimum distance, among others. evaluation code}, construction which allows to study codes using tools of algebraic geometry commutative algebra. generate im...

Algebraic space–time coding allows for reliable data exchange across fading multiple-input multiple-output channels. A powerful technique for decoding space–time codes is Maximum-Likelihood (ML) decoding, but well-performing and widely-used codes such as the Golden code often suffer from high ML-decoding complexity. In this article, a recursive algorithm for decoding general algebraic space–tim...

In this paper, we construct new families of convolutional codes. Such codes are obtained by means of algebraic geometry codes. Additionally, more families of convolutional codes are constructed by means of puncturing, extending, expanding and by the direct product code construction applied to algebraic geometry codes. The parameters of the new convolutional codes are better than or comparable t...

The systematics of indices of physico-chemical properties of codons and amino acids across the genetic code are examined. Using a simple numerical labelling scheme for nucleic acid bases, A=(-1,0), C=(0,-1), G=(0,1), U=(1,0), data can be fitted as low order polynomials of the six coordinates in the 64-dimensional codon weight space. The work confirms and extends the recent studies by Siemion et...

This report presents ways to provide automated support for code generator veriication as described by Markus M uller-Olm in MO95] using the Prototype Veriication System (PVS, see Rus93]).

A new numerical integration code (COLDDAE) for general linear differentialalgebraic equations (DDAEs) of retarded and neutral type is discussed. The implementation is based on the regularization technique introduced in [13]. In the single delay case, the code can handle noncausal systems, i.e., systems, where the solution at the current time does not only depend on the system at the past and cu...

In this paper, a new algebraic soft-decision decoding algorithm for Reed-Solomon code is presented. It is based on rational interpolation and the interpolation points are constructed by Berlekamp-Messay algorithm. Unlike the traditional Kötter-Vardy algorithm, new algorithm needs interpolation for two smaller multiplicity matrixes, due to the corresponding factorization algorithm for re-constru...

Reed-Solomon and BCH codes were considered as kernels of polar codes by Mori and Tanaka in [6] and Korada, Şaşoğlu, and Urbanke in [4] to create polar codes with large exponents. For codes of length l ≤ q, Mori and Tanaka showed Reed-Solomon codes give the best possible exponent, where q is the size of the input alphabet. However, considering larger matrices over Fq yields better exponents for ...

Querying and analyzing source code interactively is a critical task in reverse engineering and program understanding. Current source code query systems lack suucient formalism and ooer limited query capabilities. In this paper, we introduce the formal framework of Source Code Algebra (SCA), and outline a source code query system based on it. SCA provides a formal data model for source code, an ...

In this paper, we propose a new coder based on the algebraic CELP(ACELP) coding technique. Our goal is to improve the quality of the obtained synthetic speech by a modification of the excitation signal of the classical coder. Such modification is accomplished by the variation of both the positions of the excitation impulses, and their amplitudes. The proposed algorithm consists of dividing the ...