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cs.IT2026
A -analogue of the rational normal curve and linearized Reed-Solomon codes
Valentina Astore, Martino Borello, Alain Couvreur +1
The relationship between linear codes in the Hamming metric and projective algebraic varieties has led to deep interactions between coding theory and algebraic geometry, with class…
cs.IT2026
Maximal quadrics over finite fields and minimal codewords of projective Reed-Muller codes
Alain Couvreur, Rati Ludhani
We study the classification of minimal codewords of projective Reed-Muller codes of order . This problem is equivalent to identifying quadrics over finite fields whose set of ra…
cs.IT2026
Decoding Algorithms for Tensor Codes
Eimear Byrne, Alain Couvreur, Lucien François
Tensor codes are a generalisation of matrix codes. Such codes are defined as subspaces of order-r tensors for which the ambient space is endowed with the tensor-rank as a metric. A…