Date of Award
Doctor of Philosophy (PhD)
Robert F. Lax
We establish an algebraic foundation to complement the improved geometric codes of Feng and Rao. Viewing linear codes as affine variety codes, we utilize the Feng-Rao minimum distance bound to construct codes with relatively large dimensions. We examine higher-dimensional affine hypersurfaces with properties similar to those of Hermitian curves. We determine a Grobner basis for the ideal of the variety of rational points on certain affine Fermat varieties. This result is applied to determine parameters of codes defined from Fermat surfaces.
Salazar, Gary Lynn, "Linear Codes Defined From Higher -Dimensional Varieties." (2000). LSU Historical Dissertations and Theses. 7295.