Topic
Generic polynomial
About: Generic polynomial is a research topic. Over the lifetime, 608 publications have been published within this topic receiving 6784 citations.
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Patent•
02 Dec 2002TL;DR: A Galois field multiply/multiply-add/multipliply accumulate system (10) as discussed by the authors includes a multiplier circuit for multiplying two polynomials with coefficients over Galois fields to obtain their product, a Galois-field linear transformer circuit responsive to the multiplier circuit, and a storage circuit for supplying to the GFLT a set of coefficients for predicting the modulo remainder for a predetermined irreducible polynomial.
Abstract: A Galois field multiply/multiply-add/multiply-accumulate system (10) includes a multiplier circuit for multiplying two polynomials with coefficients over a Galois field to obtain their product; a Galois field linear transformer circuit responsive to the multiplier circuit for predicting the modulo remainder of the polynomial product for an irreducible polynomial; storage circuit for supplying to the Galois field linear transformer circuit a set of coefficient for predicting the modulo remainder for a predetermined irreducible polynomial; and a Galois field adder circuit for adding the product of the multiplier circuit with a third polynomial with coefficients over a Galois field for performing the multiplication and add operations in a single cycle.
29 citations
TL;DR: In this paper, it was shown that a general polynomial vector ( f 1, f 2, f 3 ) in three homogeneous variables of degrees ( 3, 3, 4 ) has a unique Waring decomposition of rank 7.
29 citations
Journal Article•
TL;DR: In this article, it was shown that any two-dimensional odd dihedral repre- sentation ½ over a finite field of characteristic p > 0 of the absolute Galois group of the rational numbers can be obtained from a Katz modular form of level N, character ² and weight k, where N is the conductor, ² is the prime-top part of the determinant and k is the so-called minimal weight of ½.
Abstract: We show that any two-dimensional odd dihedral repre- sentation ½ over a finite field of characteristic p > 0 of the absolute Galois group of the rational numbers can be obtained from a Katz modular form of level N, character ² and weight k, where N is the conductor, ² is the prime-to-p part of the determinant and k is the so-called minimal weight of ½ In particular, k = 1 if and only if ½ is unramified at p Direct arguments are used in the exceptional cases, where general results on weight and level lowering are not available
29 citations
TL;DR: An algorithm is given for the determination of the finitely many primes such that the image of the modular Galois representations attached to a weight 2 newform on ?
29 citations
TL;DR: In this paper, it was shown that the Galois group Gal(K/Q ) is the full symmetric group on d symbols for various values of k and level 1.
28 citations