Algebraic Coding and Cryptography
Seminar Series

Online Event

ACCESS is a joint effort designed to highlight world-class research in coding theory, cryptography, and related areas and to encourage collaboration among its participants.

Next seminar
June 18

Maria Bras Amoros
Universitat Rovira i Virgili

(@ by Guille Mendía) 

Self-orthogonal flags of cades and translation of flags of algebraic geometry codes

Abstracts. A flag $C_0 \subsetneq C_1 \cdots \subsetneq C_s \subsetneq \fq^n $ of linear codes is said to be self-orthogonal if the duals of the codes in the flag satisfy $C_{i}^\perp=C_{s-i}$, and it is said to satisfy the isometry-dual property with respect to an isometry vector ${\bf x}$ if $C_i^\perp={\bf x} C_{s-i}$ for $i=1, \dots, s$.

We characterize complete (i.e. $s=n$) flags with the isometry-dual property by means of the existence of a word with non-zero coordinates in a certain linear subspace of $\fq^n$. For flags of algebraic geometry (AG) codes we prove a so-called translation property of isometry-dual flags and give a construction of complete self-orthogonal flags, providing examples of self-orthogonal flags over some maximal function fields.  At the end we characterize the divisors giving the isometry-dual property and the related isometry vectors showing that for each function field there is only a finite number of isometry vectors and that they are related by cyclic repetitions.

This is a joint work with Alonso S. Castellanos and Luciane Quoos

Biography. Maria Bras Amoros is a Professor at Universitat Rovira i Virgili in Tarragona. She received the Ph.D. degree in applied mathematics from the Universitat Politècnica de Catalunya in 2003. Part of her doctoral and postdoctoral work was developed at San Diego State University, California. She has been with the Universitat Politècnica de Catalunya and the Universitat Autònoma de Barcelona, and is currently with the Universitat Rovira i Virgili in Tarragona. Her main research interests are in the area of coding theory and discrete mathematics.

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Organizing team

Jean-Francois Biasse - University of South Florida

Hiram Lopez - Virginia Tech

Felice Manganiello - Clemson University

Gretchen Matthews - Virginia Tech

Edoardo Persichetti - Florida Atlantic University

Material made avaliable to us by the speakers will be posted in the archive page.  

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