An upper bound of Singleton type for componentwise products of linear codes

Abstract

We give an upper bound that relates the minimum weight of a nonzero componentwise product of codewords from some given number of linear codes, with the dimensions of these codes. Its shape is a direct generalization of the classical Singleton bound.

9 pages; major improvements in v3: now works for an arbitrary number of codes, and the low-weight codeword can be taken in product form; submitted to IEEE Trans. Inform. Theory

References in corpus (1)

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

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• Algebraic geometry codes and some applications