We give new improvements to the Chudnovsky-Chudnovsky method that provides upper bounds on the bilinear complexity of multiplication in extensions of finite fields through interpolation on algebraicâ€¦ (More)

We give an upper bound that relates the dimensions of some given number of linear codes, with the minimum distance of their componentwise product. A typical result is as follows: given t linear codesâ€¦ (More)

In this text we develop some aspects of Harder-Narasimhan theory, slopes, semistability and canonical filtration, in the setting of combinatorial lattices. Of noticeable importance is theâ€¦ (More)

In this text we develop the formalism of products and powers of linear codes under componentwise multiplication. As an expanded version of the authorâ€™s talk at AGCT-14, focus is put mostly on basicâ€¦ (More)

If <i>C</i> is a binary linear code, let <i>C</i><sup>〈2〉</sup> be the linear code spanned by intersections of pairs of codewords of <i>C</i>. We construct an asymptotically good familyâ€¦ (More)

We propose a new classification of multiple antenna channels. The classification is performed in the space of Hermitian forms defined by the channel representation. We introduce a geodesic metricâ€¦ (More)

2009 IEEE International Symposium on Informationâ€¦

2009

Our motivation is the design of space-time coding which is optimal under both maximum likelihood and iterative decoding. We describe the construction of new full-rate space-time codes withâ€¦ (More)

One of the most powerful tools to derive lower bounds in extremal combinatorics is the so called probabilistic method [1]. Roughly speaking, to prove the existence of an object of a given sizeâ€¦ (More)