On the Dimension of AG Trace Codes
Phong Le, Sunil Chetty
TL;DR
This paper establishes conditions for calculating the dimension of q-ary trace codes derived from algebraic-geometric codes, introducing dimension reduction techniques for associated function spaces.
Contribution
It provides a general formula for the dimension of these trace codes and introduces new methods for reducing dimensions of related function spaces.
Findings
Derived conditions for the dimension formula
Introduced dimension reducing methods
Enhanced understanding of algebraic-geometric trace codes
Abstract
We shall derive conditions in which a general formula for the dimension of q-ary trace codes induced by algebraic-geometric codes. Significant to this result are several dimension reducing methods for the underlying functions spaces associated to q-ary trace codes.
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Taxonomy
TopicsCoding theory and cryptography · Advanced Data Storage Technologies · Cellular Automata and Applications