A note on diagonal and Hermitian hypersurfaces

Ian  Blake; V. Kumar Murty; Hamid  Usefi

doi:10.3934/amc.2016039

Article Contents

2016, Volume 10, Issue 4: 753-764. Doi: 10.3934/amc.2016039

This issue Previous Article An extension of binary threshold sequences from Fermat quotients Next Article Construction and number of self-dual skew codes over $\mathbb{F}_{p^2}$

A note on diagonal and Hermitian hypersurfaces

1.
Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, BC, V6T 1Z4
2.
Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, Canada M5S 2E4
3.
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL, A1C 5S7

Received: October 2014

Revised: August 2015

Published: November 2016

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Abstract

Aspects of the properties, enumeration and construction of points on diagonal and Hermitian hypersurfaces have been considered extensively in the literature and are further considered here. The zeta function of diagonal hypersurfaces is given as a direct result of the work of Wolfmann. Recursive construction techniques for the set of rational points of Hermitian hypersurfaces are of interest. The relationship of these techniques here to the construction of codes on hypersurfaces is briefly noted.

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Mathematics Subject Classification: Primary: 11T71, 94B27; Secondary: 14G10, 14G50.

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