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Artin-Schreier Families And 2-D Cycle Codes, Cem Guneri
Artin-Schreier Families And 2-D Cycle Codes, Cem Guneri
LSU Doctoral Dissertations
We start with the study of certain Artin-Schreier families. Using coding theory techniques, we determine a necessary and sufficient condition for such families to have a nontrivial curve with the maximum possible number of rational points over the finite field in consideration. This result produces several nice corollaries, including the existence of certain maximal curves; i.e., curves meeting the Hasse-Weil bound.We then present a way to represent two-dimensional (2-D) cyclic codes as trace codes starting from a basic zero set of its dual code. This representation enables us to relate the weight of a codeword to the number of rational …
Bounding The Wild Set (Counting The Minimum Number Of Wild Primes In Hilbert Symbol Equivalent Number Fields), Marius M. Somodi
Bounding The Wild Set (Counting The Minimum Number Of Wild Primes In Hilbert Symbol Equivalent Number Fields), Marius M. Somodi
LSU Doctoral Dissertations
This dissertation makes a contribution to the study of Witt rings of quadratic forms over number fields. To every pair of algebraic number fields with isomorphic Witt rings one can associate a number, called the minimum number of wild primes. The situation is particularly nice when this number is 0; often it is not 0. Earlier investigations have established lower bounds for this number. In this dissertation an analysis is presented that expresses the minimum number of wild primes in terms of the number of wild dyadic primes. This formula not only gives immediate upper bounds, but can be considered …