## View abstract

### Session S24 - Symbolic Computation: Theory, Algorithms and Applications

Tuesday, July 13, 16:30 ~ 16:55 UTC-3

## Walsh-Hadamard transforms of generalized $p$-ary functions and $C$-finite sequences

### Luis Medina

#### University of Puerto Rico, Rio Piedras, Puerto Rico   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloakf280a2c8ae1181d746b13b1671226a56').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addyf280a2c8ae1181d746b13b1671226a56 = 'l&#117;&#105;s.m&#101;d&#105;n&#97;17' + '&#64;'; addyf280a2c8ae1181d746b13b1671226a56 = addyf280a2c8ae1181d746b13b1671226a56 + '&#117;pr' + '&#46;' + '&#101;d&#117;'; var addy_textf280a2c8ae1181d746b13b1671226a56 = 'l&#117;&#105;s.m&#101;d&#105;n&#97;17' + '&#64;' + '&#117;pr' + '&#46;' + '&#101;d&#117;';document.getElementById('cloakf280a2c8ae1181d746b13b1671226a56').innerHTML += '<a ' + path + '\'' + prefix + ':' + addyf280a2c8ae1181d746b13b1671226a56 + '\'>'+addy_textf280a2c8ae1181d746b13b1671226a56+'<\/a>';

In this talk we show that Walsh-Hadamard transformations of generalized $p$-ary functions whose components are symmetric, rotation symmetric or a combination or concatenation of them are $C$-finite sequences. This result generalized many of the known results for regular $p$-ary functions. We also present a study of the roots of the characteristic polynomials related to these sequences and show that properties like balancedness and being bent are not shared by the underline $p$-ary functions.

Joint work with Leonid B. Sepúlveda (University of Puerto Rico, Rio Piedras) and César Serna-Rapello (University of Puerto Rico, Rio Piedras).