Coset bounds for algebraic geometric codes

Details Coset bounds for algebraic geometric codes Coset bounds for algebraic geometric codes

2008-10-15

arxiv.org/abs/0810.2789v1

Mathematics

Number Theory

36 pages

Scientific paper

For a given curve X and divisor class C, we give lower bounds on the degree of a divisor A such that A and A-C belong to specified semigroups of divisors. For suitable choices of the semigroups we obtain (1) lower bounds for the size of a party A that can recover the secret in an algebraic geometric linear secret sharing scheme with adversary threshold C, and (2) lower bounds for the support A of a codeword in a geometric Goppa code with designed minimum support C. Our bounds include and improve both the order bound and the floor bound. The bounds are illustrated for two-point codes on general Hermitian and Suzuki curves.

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