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We indicate a strategy in order to construct bilinear multiplication algorithms of type Chudnovsky in large extensions of any finite field. In particular, using the symmetric version of the generalization of Randriambololona specialized on the elliptic curves, we show that it is possible to construct such algorithms with low bilinear complexity. More precisely, if we only consider the Chudnovsky-type algorithms of type symmetric elliptic, we show that the symmetric bilinear complexity of these algorithms is in where n corresponds to the extension degree, and is the iterated logarithm. Moreover, we show that the construction of such algorithms can be done in time polynomial in n. Finally, applying this method we present the effective construction, step by step, of such an algorithm of multiplication in the finite field 픽357. [ABSTRACT FROM AUTHOR]

We give a simple decoding algorithm to decode linear cyclic codes of odd length over the ring [Mathematical Expression Omitted], where [u.sup.2] = 0. A spectral representation of the cyclic codes over R is given and a BCH-like bound is given for the Lee distance of the codes. The ring R shares many properties of [Z.sub.4] and [F.sub.4] and admits a linear "Gray map." Index Terms - Codes over rings, cyclic codes, Gray map, self-dual codes.

Presents information on a study which introduced a decoding algorithm for linear cyclic codes. Spectral representation of cyclic codes; Information on the decoding algorithm; Conclusions.

Presents a method for computing the complete weight distribution of translates of linear codes over Z4. Properties of linear codes over Z4; Properties of Galois rings over Z4; Families of codes; Translation of linear codes using the MacWilliams transform; Conclusions.