## View abstract

### Session S29 - Theory and Applications of Coding Theory

Tuesday, July 13, 12:00 ~ 12:25 UTC-3

## The Generalized Covering Radii of Linear Codes

### Marcelo Firer

#### Unicamp, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloakddaac9b4175cbed09fdf2a2f2ca3ff5d').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addyddaac9b4175cbed09fdf2a2f2ca3ff5d = 'mf&#105;r&#101;r' + '&#64;'; addyddaac9b4175cbed09fdf2a2f2ca3ff5d = addyddaac9b4175cbed09fdf2a2f2ca3ff5d + '&#117;n&#105;c&#97;mp' + '&#46;' + 'br'; var addy_textddaac9b4175cbed09fdf2a2f2ca3ff5d = 'mf&#105;r&#101;r' + '&#64;' + '&#117;n&#105;c&#97;mp' + '&#46;' + 'br';document.getElementById('cloakddaac9b4175cbed09fdf2a2f2ca3ff5d').innerHTML += '<a ' + path + '\'' + prefix + ':' + addyddaac9b4175cbed09fdf2a2f2ca3ff5d + '\'>'+addy_textddaac9b4175cbed09fdf2a2f2ca3ff5d+'<\/a>';

In this work we generalize the concept of covering radius, introducing the $r$-covering radii of a linear code. The first part of the work present several equivalent definitions, that explores different aspects of the subject: combinatorial, geometric and algebraic notions. We describe the connection of the generalized covering radii with generalized Hamming weights and produce some asymptotic bounds that shows its relevance for application to database linear querying.

Joint work with Dor Elimelech and Moshe Schwartz (Ben Gurion University, Israel)..