Let F_qbe afinite field with q=pmelements,where pis an odd prime and mis apositive integer.Here,let D_0={(x_1,x_2)∈F_q^2\{(0,0)}:Tr(x_1^(pk1+1)+x_2^(pk2+1))=c},where c∈F_q,Tr is the trace function fromFF_qtoFpand m/...Let F_qbe afinite field with q=pmelements,where pis an odd prime and mis apositive integer.Here,let D_0={(x_1,x_2)∈F_q^2\{(0,0)}:Tr(x_1^(pk1+1)+x_2^(pk2+1))=c},where c∈F_q,Tr is the trace function fromFF_qtoFpand m/(m,k_1)is odd,m/(m,k_2)is even.Define ap-ary linear code C_D =c(a_1,a_2):(a_1,a_2)∈F_q^2},where c(a_1,a_2)=(Tr(a_1x_1+a_2x_2))_((x1,x2)∈D).At most three-weight distributions of two classes of linear codes are settled.展开更多
Let F be a non-archimedean local field of characteristic 0 and(?)a nontrivial additive character.Weil first defined the Weil indexγ(a,(?))(a∈F~*)in his famous paper,from which we know thatγ(a,(?))γ(b,(?))=γ(ab,(...Let F be a non-archimedean local field of characteristic 0 and(?)a nontrivial additive character.Weil first defined the Weil indexγ(a,(?))(a∈F~*)in his famous paper,from which we know thatγ(a,(?))γ(b,(?))=γ(ab,(?))γ(1,(?))(a,b)andγ(a,(?))~4 =(-1,-1),where(a,b)is the Hilbert symbol for F.The Weil index plays an important role in the theory of theta series and in the general representation theory.In this paper,we establish an identity relating the Weil indexγ(a,(?))and the Gauss sum.展开更多
这份报纸与在有限领域 \ 上灵活的几个参数被奉献给半偏好函数的学习(\mathbb { F }_{ 2 ^ n }\) 。在\上定义的布尔功能( \mathbb { F }_{ 2 ^ n }\)表格$f_{一， b }^{(r)}(x)= Tr_1 ^ n (斧子^{ r ( 2 ^ m - 1 )})+ Tr_1 ^ 4 ( bx ^{...这份报纸与在有限领域 \ 上灵活的几个参数被奉献给半偏好函数的学习(\mathbb { F }_{ 2 ^ n }\) 。在\上定义的布尔功能( \mathbb { F }_{ 2 ^ n }\)表格$f_{一， b }^{(r)}(x)= Tr_1 ^ n (斧子^{ r ( 2 ^ m - 1 )})+ Tr_1 ^ 4 ( bx ^{ \tfrac {{ 2 ^ n - 1 }}{ 5 }})$并且表格$g_{一， b ， c ， d }^{( r ， s )}(x)= Tr_1 ^ n (斧子^{ r ( 2 ^ m - 1 )})+ Tr_1 ^ 4 ( bx ^{ \tfrac {{ 2 ^ n - 1 }}{ 5 }})+ Tr_1 ^ n ( cx ^{( 2 ^ m - 1 ) \tfrac { 1 }{ 2 }+ 1 })+ Tr_1 ^ n ( dx ^{( 2 ^ m - 1 ) s + 1 })$在哪儿 n = 2m ， m 2 (现代派 4 )，一， c \( \mathbb { F }_{ 16 }\)，并且 b \( \mathbb { F } _2 \)， d \( \mathbb { F } _2 \)，在构造半偏好 f 的新班被调查象 Kloosterman 和那样的一些典型的和和 Weil 和被采用决定上述功能是否是半偏好。展开更多
文摘Let F_qbe afinite field with q=pmelements,where pis an odd prime and mis apositive integer.Here,let D_0={(x_1,x_2)∈F_q^2\{(0,0)}:Tr(x_1^(pk1+1)+x_2^(pk2+1))=c},where c∈F_q,Tr is the trace function fromFF_qtoFpand m/(m,k_1)is odd,m/(m,k_2)is even.Define ap-ary linear code C_D =c(a_1,a_2):(a_1,a_2)∈F_q^2},where c(a_1,a_2)=(Tr(a_1x_1+a_2x_2))_((x1,x2)∈D).At most three-weight distributions of two classes of linear codes are settled.
文摘Let F be a non-archimedean local field of characteristic 0 and(?)a nontrivial additive character.Weil first defined the Weil indexγ(a,(?))(a∈F~*)in his famous paper,from which we know thatγ(a,(?))γ(b,(?))=γ(ab,(?))γ(1,(?))(a,b)andγ(a,(?))~4 =(-1,-1),where(a,b)is the Hilbert symbol for F.The Weil index plays an important role in the theory of theta series and in the general representation theory.In this paper,we establish an identity relating the Weil indexγ(a,(?))and the Gauss sum.
基金supported by the National Natural Science Foundation of China under Grant No.11371011
文摘这份报纸与在有限领域 \ 上灵活的几个参数被奉献给半偏好函数的学习(\mathbb { F }_{ 2 ^ n }\) 。在\上定义的布尔功能( \mathbb { F }_{ 2 ^ n }\)表格$f_{一， b }^{(r)}(x)= Tr_1 ^ n (斧子^{ r ( 2 ^ m - 1 )})+ Tr_1 ^ 4 ( bx ^{ \tfrac {{ 2 ^ n - 1 }}{ 5 }})$并且表格$g_{一， b ， c ， d }^{( r ， s )}(x)= Tr_1 ^ n (斧子^{ r ( 2 ^ m - 1 )})+ Tr_1 ^ 4 ( bx ^{ \tfrac {{ 2 ^ n - 1 }}{ 5 }})+ Tr_1 ^ n ( cx ^{( 2 ^ m - 1 ) \tfrac { 1 }{ 2 }+ 1 })+ Tr_1 ^ n ( dx ^{( 2 ^ m - 1 ) s + 1 })$在哪儿 n = 2m ， m 2 (现代派 4 )，一， c \( \mathbb { F }_{ 16 }\)，并且 b \( \mathbb { F } _2 \)， d \( \mathbb { F } _2 \)，在构造半偏好 f 的新班被调查象 Kloosterman 和那样的一些典型的和和 Weil 和被采用决定上述功能是否是半偏好。
基金Supported by Science Research Project of Hubei Provincial Department of Education(No.B2020150)Natural Science Project of Xiaogan City(No.XGKJ2020010045)Technology Creative Project of Excellent Middle and Young Team of Hubei Province(No.T201920)。
