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

填料

neologism

Exponentiation in finite fields: Theory and practice,Finally we want to outline the main properties for a fast software exponentiation algorithm in .for large .∈ℕ:

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florid

挫败

Elementary approximation of exponentials of Lie polynomials,Let .=.(..,..., x.) be a graded Lie algebra generated by ..,..., ... In this paper, we show that for any element . in . and any order ., exp(.) may be approximated at the order . by a finite product of elementary factors exp(λ.,x.,). We give an explicit construction that avoids any calculation in the Lie algebra.

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阴郁

,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.

附录

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.

分解

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.

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