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- Trygve Johnsen, Hugues Verdure
- IEEE Transactions on Information Theory
- 2017

We define generalized Hamming weights for almost affine codes. We show that this definition is natural, since we can extend some well-known properties of the generalized Hamming weights for linear codes, to almost affine codes. In addition, we discuss the duality of almost affine codes, and of the smaller class of multilinear codes.

- Trygve Johnsen, Keisuke Shiromoto, Hugues Verdure
- Des. Codes Cryptography
- 2016

The theorem of Jung establishes a relation between circumradius and diameter of a convex body. The half of the diameter can be interpreted as the maximum of circumradii of all 1-dimensional sections or 1-dimensional orthogonal projections of a convex body. This point of view leads to two series of j-dimensional circumradii, defined via sections orâ€¦ (More)

- Trygve Johnsen, Jan Roksvold, Hugues Verdure
- Discrete Mathematics
- 2016

Generalizing polynomials previously studied in the context of linear codes, we define weight polynomials and an enumerator for a matroid M . Our main result is that these polynomials are determined by Betti numbers associated with N0-graded minimal free resolutions of the Stanley-Reisner ideals of M and so-called elongations of M . Generalizing Greeneâ€™sâ€¦ (More)

- Trygve Johnsen, Hugues Verdure
- ArXiv
- 2017

We describe a two-party wire-tap channel of type II in the framework of almost affine codes. Its cryptological performance is related to some relative profiles of a pair of almost affine codes. These profiles are analogues of relative generalized Hamming weights in the linear case.

- Trygve Johnsen, Hugues Verdure
- Des. Codes Cryptography
- 2014

Given a constant weight linear code, we investigate its weight hierarchy and the Stanley-Reisner resolution of its associated matroid regarded as a simplicial complex. We also exhibit conditions on the higher weights sufficient to conclude that the code is of constant weight.

- Trygve Johnsen, Hugues Verdure
- ICMCTA
- 2017

- Trygve Johnsen, Hugues Verdure
- Applicable Algebra in Engineering, Communicationâ€¦
- 2012

To each linear code $$C$$ over a finite field we associate the matroid $$M(C)$$ of its parity check matrix. For any matroid $$M$$ one can define its generalized Hamming weights, and if a matroid is associated to such a parity check matrix, and thus of type $$M(C)$$ , these weights are the same as those of the code $$C$$ . In our main result we show how theâ€¦ (More)

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