Calculs de Certaines Sommes de Gauss

Langevin, Philippe

doi:10.1006/jnth.1997.2078

Cited by 40 publications

(26 citation statements)

References 9 publications

(8 reference statements)

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“…It is called the "index r case". In 1970's-2000's, the Gauss sums in the index r =2 case have been studied and evaluated explicitly in a series of papers [9,[12][13][14]17]. And since 2005, the case of index r = 4 has been studied [5,6,19].…”

Section: Lemma 22 (Seementioning

confidence: 99%

“…(For the details on the relationship between Hamming weight distribution of irreducible cyclic codes and Gauss sums, we refer to [1,2,11,15,18] or [3,Chapter 11.7].) In 1997, Langevin [9], as the generalization of [13], gave the evaluation of Gauss sums in the index 2 case for N = l r , where l is an odd prime, r 1. One year later, Mbodj [12], as the generalization of [17], gave the evaluation of Gauss sums in the index 2 case for N = l r1 1 l r2 2 , where l 1 , l 2 are distinct odd primes, r 1 , r 2 1.…”

Section: Introductionmentioning

confidence: 99%

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Complete solving of explicit evaluation of Gauss sums in the index 2 case

Yang

Xia

2010

Sci. China Math.

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Let p be a prime number, N be a positive integer such that gcd(N, p) = 1, q = p f where f is the multiplicative order of p modulo N . Let χ be a primitive multiplicative character of order N over finite field Fq. This paper studies the problem of explicit evaluation of Gauss sums G(χ) in the "index 2 case" (i.e. [(Z/N Z) * : p ] = 2). Firstly, the classification of the Gauss sums in the index 2 case is presented. Then, the explicit evaluation of Gauss sums G(χ λ ) (1 λ N − 1) in the index 2 case with order N being general even integer (i.e. N = 2 r · N 0 , where r, N 0 are positive integers and N 0 3 is odd) is obtained. Thus, combining with the researches before, the problem of explicit evaluation of Gauss sums in the index 2 case is completely solved.

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Section: Lemma 22 (Seementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Complete solving of explicit evaluation of Gauss sums in the index 2 case

Yang

Xia

2010

Sci. China Math.

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“…They have only been computed when the subgroup generated by 2 in (Z/dZ) * has index 2 or contains −1, see [1,6,11,15]. For applications of these computations to irreducible codes see [1][2][3]12,14].…”

Section: Introductionmentioning

confidence: 99%

Sums of Gauss sums and weights of irreducible codes

Fitzgerald

Yucas

2005

Finite Fields and Their Applications

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“…For certain special characters, the associated Gauss sums have been evaluated (see [1,3,4,7]). But, in general, it is hard to determine these sums explicitly.…”

Section: Introductionmentioning

confidence: 99%

“…In [9], this case was studied under the assumption that p"2 and m is a product of two distinct primes. In this index 2 case the Gauss sums have been calculated if m"l in [1], and if m"lP in [7], where l is a prime such that l'3, l,3 (mod 4).…”

Section: Introductionmentioning

confidence: 99%