Abstract:
I will introduce a new wide class of error-correcting codes called non-split toric codes. These codes are a natural generalization of usual (i.e., split) toric codes, where non-split (over a finite field) algebraic tori and toric varieties are taken instead of split ones. More precisely, I will construct new cyclic codes, which are non-split toric ones on the del Pezzo surface of degree 6 and Picard number 1. For this purpose I will produce many results for this surface and its anticanonical linear system. Finally, I will also compute parameters of the new codes, which prove to attain current lower bounds at least for small finite fields.
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