Title: Toric Codes, Multiplicative Structure and Decoding,
Abstract: Long linear codes constructed from toric varieties over finite fields, their
multiplicative structure and decoding. The main theme is the inherent
multiplicative structure on toric codes. The multiplicative structure allows
for \emph{decoding}, resembling the decoding of Reed-Solomon codes and aligns
with decoding by error correcting pairs. We have used the multiplicative
structure on toric codes to construct linear secret sharing schemes with
\emph{strong multiplication} via Massey's construction generalizing the Shamir
Linear secret sharing shemes constructed from Reed-Solomon codes. We have
constructed quantum error correcting codes from toric surfaces by the
Calderbank-Shor-Steane method.