# A Family of p-ary Binomial Bent Functions

## 抄録

For a prime <i>p</i> with <i>p</i> ≡ 3(mod 4) and an odd number <i>m</i>, the Bentness of the <i>p</i>-ary binomial function $f_{a,b}(x)={\\rm Tr}_{1}^n(ax^{p^m-1})+{\\rm Tr}_{1}^2(bx^{\\frac{p^n-1}{4}})$ is characterized, where <i>n</i>=2<i>m</i>, $a\\in \\bF_{p^n}^*$, and $b\\in \\bF_{p^2}^*$. The necessary and sufficient conditions of ƒ<sub><i>a</i>,<i>b</i></sub>(<i>x</i>) being Bent are established respectively by an exponential sum and two sequences related to <i>a</i> and <i>b</i>. For the special case of <i>p</i>=3, we further characterize the Bentness of the ternary function ƒ<sub><i>a</i>,<i>b</i></sub>(<i>x</i>) by the Hamming weight of a sequence.

## 収録刊行物

• IEICE transactions on fundamentals of electronics, communications and computer sciences

IEICE transactions on fundamentals of electronics, communications and computer sciences 94(9), 1868-1872, 2011-09-01

The Institute of Electronics, Information and Communication Engineers

## 各種コード

• NII論文ID(NAID)
10030190926
• NII書誌ID(NCID)
AA10826239
• 本文言語コード
ENG
• 資料種別
SHO
• ISSN
09168508
• データ提供元
CJP書誌  J-STAGE

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