44,359 research outputs found
Information Sets of Multiplicity Codes
We here provide a method for systematic encoding of the Multiplicity codes
introduced by Kopparty, Saraf and Yekhanin in 2011. The construction is built
on an idea of Kop-party. We properly define information sets for these codes
and give detailed proofs of the validity of Kopparty's construction, that use
generating functions. We also give a complexity estimate of the associated
encoding algorithm.Comment: International Symposium on Information Theory, Jun 2015, Hong-Kong,
China. IEE
Fast systematic encoding of multiplicity codes
We present quasi-linear time systematic encoding algorithms for multiplicity
codes. The algorithms have their origins in the fast multivariate interpolation
and evaluation algorithms of van der Hoeven and Schost (2013), which we
generalise to address certain Hermite-type interpolation and evaluation
problems. By providing fast encoding algorithms for multiplicity codes, we
remove an obstruction on the road to the practical application of the private
information retrieval protocol of Augot, Levy-dit-Vehel and Shikfa (2014)
List decoding of a class of affine variety codes
Consider a polynomial in variables and a finite point ensemble . When given the leading monomial of with respect to
a lexicographic ordering we derive improved information on the possible number
of zeros of of multiplicity at least from . We then use this
information to design a list decoding algorithm for a large class of affine
variety codes.Comment: 11 pages, 5 table
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