## View abstract

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

Wednesday, July 14, 13:30 ~ 13:55 UTC-3

## A family of codes with locality containing optimal codes

### Victor Gonzalo Lopez Neumann

#### Universidade Federal de Uberlândia, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak1b784402e5f7943c3e1d6ebfbc17c5c6').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy1b784402e5f7943c3e1d6ebfbc17c5c6 = 'v&#105;ct&#111;r.n&#101;&#117;m&#97;nn' + '&#64;'; addy1b784402e5f7943c3e1d6ebfbc17c5c6 = addy1b784402e5f7943c3e1d6ebfbc17c5c6 + '&#117;f&#117;' + '&#46;' + 'br'; var addy_text1b784402e5f7943c3e1d6ebfbc17c5c6 = 'v&#105;ct&#111;r.n&#101;&#117;m&#97;nn' + '&#64;' + '&#117;f&#117;' + '&#46;' + 'br';document.getElementById('cloak1b784402e5f7943c3e1d6ebfbc17c5c6').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy1b784402e5f7943c3e1d6ebfbc17c5c6 + '\'>'+addy_text1b784402e5f7943c3e1d6ebfbc17c5c6+'<\/a>';

Locally recoverable codes were introduced by Gopalan et al.\ in 2012, and in the same year, Prakash et al.\ introduced the concept of codes with locality, which are a type of locally recoverable codes. In this work, we introduce a new family of codes with locality, which are subcodes of a certain family of evaluation codes. We determine the dimension of these codes, and also bounds for the minimum distance. We present the true values of the minimum distance in special cases, and also show that elements of this family are optimal codes'', as defined by Prakash et al.

Joint work with Bruno Andrade (Universidade Federal de Uberlândia, Brazil) and Cícero Carvalho (Universidade Federal de Uberlândia, Brazil).