AbstractThe connection between bilinear complexity and error-correcting codes, discovered by Brockett and Dobkin in 1973, yields lower bounds on the maximal ranks of tensors with a given shape. The resulting bounds are linear, and thus interesting only for “unbalanced” shapes like (n,n,2) and (n,n,n2−k) with k⩽n. As an example, for odd n the maximal rank of (n,n,2)-tensors is larger over Z2 than over an algebraic closure of Z2
AbstractUpper bounds on the typical rank R(n, m, l) of tensors ( = maximal border rank = rank of alm...
Tensor codes were introduced by Roth in 1991 and defined to be subspaces of r-tensors where the ambi...
We prove that the slice rank of a 3-tensor (a combinatorial notion introduced by Tao in the context ...
It is shown that the maximal rank of m × n × ( m n - k ) tensors with k min {( m - 1 ) 2 /2 , ( ...
AbstractThe typical rank (= maximal border rank) of tensors of a given size and the set of optimal b...
The subject of the present book is naturally divided into three parts. The first part (Chapter 1) de...
In this thesis, geometric representations of rank-metric codes have been examined as well as their c...
International audienceWe establish new upper bounds about symmetric bilinear complexity in any exten...
AbstractThe number of nonscalar multiplications required to evaluate a general family of bilinear fo...
The set of all subspaces of F-q(n) is denoted by P-q(n). The subspace distance d(S)(X, Y) = dim(X) +...
In this paper we construct infinite families of non-linear maximum rank distance codes by using the ...
It is shown that the parameters of a linear code over Fq of length n, dimension k, minimum weight d,...
AbstractThe border rank of a nondegenerate m×n×(mn−q) tensor over the complex field is mn−q provided...
The set of all subspaces of Fqn is denoted by Pq(n). The subspace distance dS(X, Y) = dim(X) + dim(Y...
We develop lower bounds on communication in the memory hierarchy or between processors for nested bi...
AbstractUpper bounds on the typical rank R(n, m, l) of tensors ( = maximal border rank = rank of alm...
Tensor codes were introduced by Roth in 1991 and defined to be subspaces of r-tensors where the ambi...
We prove that the slice rank of a 3-tensor (a combinatorial notion introduced by Tao in the context ...
It is shown that the maximal rank of m × n × ( m n - k ) tensors with k min {( m - 1 ) 2 /2 , ( ...
AbstractThe typical rank (= maximal border rank) of tensors of a given size and the set of optimal b...
The subject of the present book is naturally divided into three parts. The first part (Chapter 1) de...
In this thesis, geometric representations of rank-metric codes have been examined as well as their c...
International audienceWe establish new upper bounds about symmetric bilinear complexity in any exten...
AbstractThe number of nonscalar multiplications required to evaluate a general family of bilinear fo...
The set of all subspaces of F-q(n) is denoted by P-q(n). The subspace distance d(S)(X, Y) = dim(X) +...
In this paper we construct infinite families of non-linear maximum rank distance codes by using the ...
It is shown that the parameters of a linear code over Fq of length n, dimension k, minimum weight d,...
AbstractThe border rank of a nondegenerate m×n×(mn−q) tensor over the complex field is mn−q provided...
The set of all subspaces of Fqn is denoted by Pq(n). The subspace distance dS(X, Y) = dim(X) + dim(Y...
We develop lower bounds on communication in the memory hierarchy or between processors for nested bi...
AbstractUpper bounds on the typical rank R(n, m, l) of tensors ( = maximal border rank = rank of alm...
Tensor codes were introduced by Roth in 1991 and defined to be subspaces of r-tensors where the ambi...
We prove that the slice rank of a 3-tensor (a combinatorial notion introduced by Tao in the context ...
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