本文選題：對(duì)角方程 + Guass和��； 參考：《南京航空航天大學(xué)》2017年碩士論文

【摘要】：設(shè)Fq為q元有限域,其中q=pf, 為素?cái)?shù),f為正整數(shù).本文主要運(yùn)用有限域上特征和與指數(shù)方程的相關(guān)理論,探究了有限域上對(duì)角方程(組)在一些特殊條件下解數(shù)的具體公式,以及對(duì)角方程(組)解數(shù)的應(yīng)用.詳細(xì)研究工作以及最終結(jié)果如下:(1)給出了形如(?)的對(duì)角方程在有限域Fq2上解數(shù)的直接公式,其中i=1 ai,c ∈Fq2*,(mi,m) = 1,mi | (q +1),mi為奇數(shù)或者q+1/mi為偶數(shù);(2)給出了形如(?)的對(duì)角方程在有限域Fq2上解數(shù)的直接公式,其中i=l c ∈ Fq*, m|(q +1), m為奇數(shù)或者q+1/m為偶數(shù);m(3)給出了形如(?)的對(duì)角方程在有限域Fq2s上解數(shù)的直接公式,其中i=1 ai ∈Fq2s*,c ∈ Fq2s, mi | (q+1);(4)探究了 Fq上對(duì)角方程組 (?),在一些特殊條件下的解數(shù)公式;(5)通過求解方程組的解數(shù),得出了當(dāng)q =2m且q8時(shí),Fq上Melas碼的覆蓋半徑為3.
[Abstract]:Let FQ be a q-element finite field, where qn p f is a prime number f is a positive integer. In this paper, by using the theory of characteristic and exponent equation on finite field, the formula of solution number of diagonal equation (group) on finite field under some special conditions and the application of diagonal equation (group) solution number are discussed. The detailed research work and the final results are as follows: (1) give the shape of (?) A direct formula for the solution of the diagonal equation on the finite field Fq2, where iG1 AIC 鈭，

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