The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
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Nesta carta, a uniformidade diferencial da função de potência f(x)=xe sobre GF(3m) é estudado, onde m≥3 é um número inteiro ímpar e $e= rac{3^m-3}{4}$. É mostrado que Δf≤3 e a função de potência não é CCZ equivalente às conhecidas. Além disso, consideramos uma família de códigos cíclicos ternários C(1,e), que é gerado por mω(x)mωe(x). Aqui, ω é um elemento primitivo de GF(3m), mω(x) e mωe(x) são polinômios mínimos de ω e ωe, respectivamente. Os parâmetros desta família de códigos cíclicos são determinados. Acontece que C(1,e) é ideal em relação ao limite do Sphere Packing.
Haode YAN
Southwest Jiaotong University
Dongchun HAN
Southwest Jiaotong University
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Haode YAN, Dongchun HAN, "New Ternary Power Mapping with Differential Uniformity Δf≤3 and Related Optimal Cyclic Codes" in IEICE TRANSACTIONS on Fundamentals,
vol. E102-A, no. 6, pp. 849-853, June 2019, doi: 10.1587/transfun.E102.A.849.
Abstract: In this letter, the differential uniformity of power function f(x)=xe over GF(3m) is studied, where m≥3 is an odd integer and $e=rac{3^m-3}{4}$. It is shown that Δf≤3 and the power function is not CCZ-equivalent to the known ones. Moreover, we consider a family of ternary cyclic code C(1,e), which is generated by mω(x)mωe(x). Herein, ω is a primitive element of GF(3m), mω(x) and mωe(x) are minimal polynomials of ω and ωe, respectively. The parameters of this family of cyclic codes are determined. It turns out that C(1,e) is optimal with respect to the Sphere Packing bound.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E102.A.849/_p
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@ARTICLE{e102-a_6_849,
author={Haode YAN, Dongchun HAN, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={New Ternary Power Mapping with Differential Uniformity Δf≤3 and Related Optimal Cyclic Codes},
year={2019},
volume={E102-A},
number={6},
pages={849-853},
abstract={In this letter, the differential uniformity of power function f(x)=xe over GF(3m) is studied, where m≥3 is an odd integer and $e=rac{3^m-3}{4}$. It is shown that Δf≤3 and the power function is not CCZ-equivalent to the known ones. Moreover, we consider a family of ternary cyclic code C(1,e), which is generated by mω(x)mωe(x). Herein, ω is a primitive element of GF(3m), mω(x) and mωe(x) are minimal polynomials of ω and ωe, respectively. The parameters of this family of cyclic codes are determined. It turns out that C(1,e) is optimal with respect to the Sphere Packing bound.},
keywords={},
doi={10.1587/transfun.E102.A.849},
ISSN={1745-1337},
month={June},}
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TY - JOUR
TI - New Ternary Power Mapping with Differential Uniformity Δf≤3 and Related Optimal Cyclic Codes
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 849
EP - 853
AU - Haode YAN
AU - Dongchun HAN
PY - 2019
DO - 10.1587/transfun.E102.A.849
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E102-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 2019
AB - In this letter, the differential uniformity of power function f(x)=xe over GF(3m) is studied, where m≥3 is an odd integer and $e=rac{3^m-3}{4}$. It is shown that Δf≤3 and the power function is not CCZ-equivalent to the known ones. Moreover, we consider a family of ternary cyclic code C(1,e), which is generated by mω(x)mωe(x). Herein, ω is a primitive element of GF(3m), mω(x) and mωe(x) are minimal polynomials of ω and ωe, respectively. The parameters of this family of cyclic codes are determined. It turns out that C(1,e) is optimal with respect to the Sphere Packing bound.
ER -