Section: New Results
Codes over rings
M. Barbier, C. Chabot and Guillaume Quintin proposed a new description for quasi–cyclic codes using the ring of matrices with polynomial entries, thus defining the new class of quasi-BCH codes. Guillaume Quintin proved that these codes can be regarded as interleaved subcodes of Reed–Solomon codes; this allowed them to define a polynomial-time decoding algorithm for quasi-BCH codes. Guillaume Quintin also generalized list decoding algorithms to codes over non commutative rings  .