Abstract We consider weighted Reed–Muller codes over point ensemble S 1×···× S m where
S i needs not be of the same size as S j. For m= 2 we determine optimal weights and …

We design the first efficient algorithms and prove new combinatorial bounds for list decoding
tensor products of codes and interleaved codes.(1) We show that for every code, the ratio of …

We consider a list decoding algorithm recently proposed by Pellikaan-Wu [8] for q-ary Reed-
Muller codes RM q (l, m, n) of length n les qm when I les q. A simple and easily accessible …

We consider multivariate polynomials and investigate how many zeros of multiplicity at least
r they can have over a Cartesian product of finite subsets of a field. Here r is any prescribed …

The research that led to this thesis was inspired by Sudan's breakthrough that demonstrated
that Reed-Solomon codes can correct more errors than previously thought. This …

La Teor´ ıa de C´ odigos busca transmitir de manera eficiente y sin errores un mensaje entre
un emisor y un receptor a trav´ es de un canal con ruido. Este ruido puede causar errores en …

We consider non-binary product codes with MDS components and their iterative row-column
algebraic decoding on the erasure channel. Both independent and block erasures are …

In [10, 11],[2],[4] and [7], Pellikaan et al., Augot et al., Dvir et al., and Geil et al., respectively,
established bounds on the number of zeros of prescribed multiplicity for multivariate …

Consider a polynomial $ F $ in $ m $ variables and a finite point ensemble $ S=
S_1\times...\times S_m $. When given the leading monomial of $ F $ with respect to a …

Let S be a finite subset of a field. For multivariate polynomials the generalized Schwartz-
Zippel bound [2],[4] estimates the number of zeros over Sx... xS counted with multiplicity. It …