## View abstract

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

Wednesday, July 14, 15:00 ~ 15:25 UTC-3

## Hermitian-Lifted Codes

### Beth Malmskog

#### Colorado College, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak44a62534c5e99e662b156604d6547177').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy44a62534c5e99e662b156604d6547177 = 'bm&#97;lmsk&#111;g' + '&#64;'; addy44a62534c5e99e662b156604d6547177 = addy44a62534c5e99e662b156604d6547177 + 'c&#111;l&#111;r&#97;d&#111;c&#111;ll&#101;g&#101;' + '&#46;' + '&#101;d&#117;'; var addy_text44a62534c5e99e662b156604d6547177 = 'bm&#97;lmsk&#111;g' + '&#64;' + 'c&#111;l&#111;r&#97;d&#111;c&#111;ll&#101;g&#101;' + '&#46;' + '&#101;d&#117;';document.getElementById('cloak44a62534c5e99e662b156604d6547177').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy44a62534c5e99e662b156604d6547177 + '\'>'+addy_text44a62534c5e99e662b156604d6547177+'<\/a>';

In recent work of Lopez, Malmskog, Matthews, Pinero-Gonzales, and Wootters, we constructed codes for local recovery of erasures with high availability and constant-bounded rate from the Hermitian curve. These new codes, called Hermitian-lifted codes, are evaluation codes with evaluation set being the set of $F_(q^2)$-rational points on the affine curve. The novelty is in terms of the functions to be evaluated; they are a special set of monomials which restrict to low degree polynomials on lines intersected with the Hermitian curve. The resulting codes are neither punctured traditional lifted codes, nor subcodes of previously defined locally recoverable codes on the Hermitian curve. This talk will introduce the codes and bounds on their parameters, and discuss questions for further research.

Joint work with Hiram Lopez, Valdez (University of Cleveland), Gretchen Matthews (Virginia Tech), Fernando Pinero-Gonzales (University of Puerto Rico Ponce) and Mary Wootters (Stanford University).