Distribution of the weights of the dual of the Melas code
type: Item
instance of: scholarly article
title: Distribution of the weights of the dual of the Melas code
zbMATH Open document ID: 0698.94009
DOI: 10.1016/0012-365X(90)90059-Q
author: Gilles Lachaud
published in: Discrete Mathematics
publication date: 1990-01-01T00:00:00Z
review text: The title of this paper suggests that the weight distribution of the dual of the Melas code is determined. However the author only gives a property of this weight distribution, using some deep results of Deligne and Katz. More precisely if \(f\) is some testfunction set \[ g_ q(w)=f((q-1- 2w)/2\sqrt{q})\text{ for} w \in [(q-1-2\sqrt{q})/2,(q-1+2\sqrt{q})/2] \] and \(\phi_ q(w)=(1/\pi q)\sqrt{4q-(q-1-2w)^ 2}\). Then: \[ (1/q^ 2)\sum_{x\in C_{k\ell}(q)}g_ q(w(x))=\int^{w^+}_{w_-}g_ q(w)\phi_ q(w)dw+O(1/\sqrt{q})\text{ when} q\to \infty \] and the constant of the O-term only depends on f. The paper contains the following misprints: p.104: middle of the page: \(z(x)=(2w(x)-(q-1))/2\sqrt{q}\) should read \(z(x)=((q-1)- 2w(x))/2\sqrt{q};\) p. 105: first formula: \(q-1+w_{k\ell}(a)\) should read: \(q-1-w_{k\ell}(a);\) p. 105: formula following Remark should read: \(w=(q-1-2\sqrt{q}z)/2;\) p. 106: first formula should read: \(\phi_ q(w)=(1/\pi q)\sqrt{4q-(q-1-2w)^ 2},\) second formula should read: \(g_ q(w)=f((q-1-2w)/2Vq).\)
Mathematics Subject Classification ID: 94B15
Mathematics Subject Classification ID: 11T23
zbMATH DE Number: 4145827
zbMATH Keywords: Kloosterman sum
zbMATH Keywords: weight distribution
zbMATH Keywords: Melas code
reviewed by: Herman J. Tiersma
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4145827