Titlebook: Applied Algebra, Algebraic Algorithms and Error-Correcting Codes; 12th International S Teo Mora,Harold Mattson Conference proceedings 1997

冒烟

Minimun distance decoding algorithms for linear codes,ve the current decision. Important examples in this class are the minimal-vectors decoding [14] and zero-neighbours decoding [16]. These two methods have some common features that enable us to introduce a general .. We formulate key properties of this decoding, which allows us to analyze known algor

Infusion

Efficient multivariate factorization over finite fields,elease 3. We give selected details of the algorithms and show several ideas that were used to improve its efficiency. Most of the improvements presented here are incorporated in Maple V Release 4..In particular, we show that we needed a general tool for implementing computations in ...., ..,..., ..]

Condescending

通便

,The symmetry group of ℤ, in the Lee space and the ℤ,,-linear codes, ℤ.-linearity. In this direction, we consider the .-dimensional Lee space of order ., that is, (ℤ., ..), as one of the most interesting spaces for coding applications.We establish the symmetry group of ℤ. for any . and . by determining its isometries.We also show that there is no cyclic subgroup of

保守

潜伏期

,Certain self-dual codes over ℤ4 and the odd Leech lattice,er, we provide a classification of length 24 double circulant Type I codes over ℤ. with minimum Euclidean weight 12. These codes determine (via Construction A.) the odd Leech lattice, which is a unique 24-dimensional odd unimodular lattice with minimum norm 3.

描绘

Codes from cocycles,ces. These . include classes of self-dual codes, quasi-twisted codes and, trivially, all the group ring codes and the group codes for the Gaussian channel. We believe this link between algebraic coding theory and low-dimensional group cohomology leads to (i) new ways to generate codes; (ii) a better

骚扰

On the ,-ary image of cyclic codes,mple encoder and can be decoded using standard equipment. Next we find all constacyclic codes whose .-ary images are by a Tschirnhaus transformation isomorphic to shortened cyclic codes. It turns out that this very large class also includes some cyclic codes. As an example the binary image of all cy

chastise

The split weight (,,, ,,) enumeration of Reed-Muller codes for ,,+,,<2,,,al form for all the relevant Boolean polynomials is derived. These results are applied to analyzing the structure and complexity of subtrellises of codewords of weights less than 2.. of Reed-Muller codes.

能量守恒

Optimal linear codes of dimension 4 over ,(5),ane arcs in .(2, 5), we prove the nonexistence of codes with parameters [215, 4, 171]. and [209, 4, 166].. This determinesthe exact value of ..(4, .) for .=166, 167, 168, 169, 170, 171. There remain 16 .‘s for which the exact value of .. (4, .) is not known.