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1. CONSTRUCTING PARTIAL MDS CODES FROM REDUCIBLE ALGEBRAIC CURVES.

Author

BOGART, TRISTRAM, HORLEMANN-TRAUTMANN, ANNA-LENA, KARPUK, DAVID, NERI, ALESSANDRO, and VELASCO, MAURICIO

Subjects
*PROJECTIVE geometry, *PROBABILITY theory, *ALGEBRAIC geometry, *COMBINATORICS, *ALGEBRAIC codes
Abstract

We propose reducible algebraic curves as a mechanism to construct partial maximum distance separable codes geometrically. We obtain new general existence results, new explicit constructions, and improved estimates on the smallest field sizes over which such codes can exist. Our results are obtained by combining ideas from projective algebraic geometry, combinatorics, and probability theory. [ABSTRACT FROM AUTHOR]

Published
2021
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