Information sets of Multiplicity codes
@article{Augot2015InformationSO, title={Information sets of Multiplicity codes}, author={Daniel Augot and Françoise Levy-dit-Vehel and Man Cuong Ng{\^o}}, journal={2015 IEEE International Symposium on Information Theory (ISIT)}, year={2015}, pages={2401-2405} }
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 Kopparty. 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.
3 Citations
Iterative erasure correcting algorithm for q-ary reed-muller codes based on local correctability
- Computer Science2016 9th International Symposium on Turbo Codes and Iterative Information Processing (ISTC)
- 2016
A novel iterative erasure correcting algorithm for q-ary RM codes based on their local correctability that provides massive parallelism and yields near ML decoding performance.
Adaptive Multiplicity Codes based PIR Protocol for Multi-Cloud Plateform Services
- Computer Science2018 IEEE 5G World Forum (5GWF)
- 2018
A Multiplicity codes based adaptive PIR protocol that is beneficial for multi cloud platform services featured by a high variability in terms of resources, as servers availabilities and storage capacity is proposed.
References
SHOWING 1-10 OF 21 REFERENCES
Information sets and partial permutation decoding for codes from finite geometries
- Computer Science, MathematicsFinite Fields Their Appl.
- 2006
List-Decoding Multiplicity Codes
- Computer ScienceTheory Comput.
- 2012
It is shown that univariate multiplicity codes of rate R over fields of prime order can be list-decoded from a (1 R e) fraction of errors in polynomial time (for constant R;e).
A Storage-Efficient and Robust Private Information Retrieval Scheme Allowing Few Servers
- Computer ScienceCANS
- 2014
This paper constructs a Byzantine robust PIR scheme using the multiplicity codes introduced by Kopparty et al.
New generalizations of the Reed-Muller codes-I: Primitive codes
- Computer ScienceIEEE Trans. Inf. Theory
- 1968
A natural generalization to the nonbinary case is presented, which also includes the Reed-Muller codes and Reed-Solomon codes as special cases and the generator polynomial is characterized and the minimum weight is established.
New generalizations of the Reed-Muller codes-II: Nonprimitive codes
- Computer ScienceIEEE Trans. Inf. Theory
- 1968
A class of nonprimitive cyclic codes quite similar in structure to the original Reed-Muller codes is presented, and it is shown that for given values of code length and rate the codes have relatively large minimum distances.
High-rate codes with sublinear-time decoding
- Computer ScienceSTOC '11
- 2011
A new family of locally decodable codes is constructed that have very efficient local decoding algorithms, and at the same time have rate approaching 1, and is called multiplicity codes, based on evaluating high degree multivariate polynomials and their derivatives.
Linear-Algebraic List Decoding for Variants of Reed–Solomon Codes
- Computer ScienceIEEE Transactions on Information Theory
- 2013
This work highlights that constructing an explicit subspace-evasive subset that has small intersection with low-dimensional subspaces-an interesting problem in pseudorandomness in its own right-could lead to explicit codes with better list-decoding guarantees.
On the efficiency of local decoding procedures for error-correcting codes
- Computer ScienceSTOC '00
- 2000
In appli ations to data storage (and also in applications to data transmission) a message is typi ally into small blo ks, and then ea h blo k is en oded separately, which allows retrieval of data stored in musi CDs and in CD-ROMs.
Enumerative combinatorics
- MathematicsSIGA
- 2008
This review of 3 Enumerative Combinatorics, by Charalambos A.good, does not support this; the label ‘Example’ is given in a rather small font followed by a ‘PROOF,’ and the body of an example is nonitalic, utterly unlike other statements accompanied by demonstrations.
List-decoding multiplicity codes,” Electronic Colloquium on Computational Complexity (ECCC)
- vol. TR12-044,
- 2012