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20122021
most citedDecoding color codes by projection onto surface codes

90 citations

Showing 2013Show all

5 papers · 1 filter

cs.IT2013

New Identities Relating Wild Goppa Codes

Alain Couvreur, Ayoub Otmani, Jean-Pierre Tillich

For a given support and a polynomial with no roots in , we prove equality between the -ary Goppa codes $Γ…

quant-ph2013★ 90 cited

Decoding color codes by projection onto surface codes

Nicolas Delfosse

We propose a new strategy to decode color codes, which is based on the projection of the error onto three surface codes. This provides a method to transform every decoding algorith…

cs.CR2013★ 7 cited

Distinguisher-Based Attacks on Public-Key Cryptosystems Using Reed-Solomon Codes

Alain Couvreur, Philippe Gaborit, Valérie Gauthier-Umaña +2

Because of their interesting algebraic properties, several authors promote the use of generalized Reed-Solomon codes in cryptography. Niederreiter was the first to suggest an insta…

math.AG2013★ 6 cited

Shimura modular curves and asymptotic symmetric tensor rank of multiplication in any finite field

Stéphane Ballet, Jean Chaumine, Julia Pieltant

We obtain new asymptotical bounds for the symmetric tensor rank of multiplication in any finite extension of any finite field $\F_q$. In this aim, we use the symmetric Chudnovsky-t…

math.AG2013★ 10 cited

New uniform and asymptotic upper bounds on the tensor rank of multiplication in extensions of finite fields

Julia Pieltant, Hugues Randriam

We obtain new uniform upper bounds for the (non necessarily symmetric) tensor rank of the multiplication in the extensions of the finite fields $\F_q$ for any prime or prime power…