The indicator of a Boolean functionMinimize Boolean functionBoolean function simplificationSimplifying...
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The indicator of a Boolean function
Minimize Boolean functionBoolean function simplificationSimplifying boolean function using boolean algebraSimplifying Boolean FunctionHow to know the boolean formula of a boolean function?Derive resultant Boolean functionsimplification of the function (boolean)Boolean function to Algebraic Normal FormFind the inverse to the boolean functionExample of univariate Boolean function
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In the paper "Componentwise APNness, Walsh uniformity of APN functions and cyclic difference sets" by Claude Carlet, it is written that: Let F be any power function on $F_{2^n}$ and $Delta _{F}={F(x)+F(x+1)+1 , xin F_{2^n}}$. In Remark 4.9, the indicator of $Delta _{F}$ is denoted by $1_{Delta _{F}}$ and in Remark 4.12, the binary sequence $a_t$ is defined as $a_t=1_{Delta _{F}}(alpha^{t})$ where $alpha$ is primitive over $F_{2^n}$ and $t=0...2^n-2$. Since there is no detailed definition of $1_{Delta _{F}}$, I do not understand what is the meaning of indicator of such a Boolean function. When I searche google, I see the definition of indicator of subsets/subspaces of finite fields.
Thanks for replys.
combinatorics finite-fields boolean-algebra cryptography
asked Mar 20 at 12:53
Kenan DOGANKenan DOGAN
425
$endgroup$
add a comment |
$begingroup$
In the paper "Componentwise APNness, Walsh uniformity of APN functions and cyclic difference sets" by Claude Carlet, it is written that: Let F be any power function on $F_{2^n}$ and $Delta _{F}={F(x)+F(x+1)+1 , xin F_{2^n}}$. In Remark 4.9, the indicator of $Delta _{F}$ is denoted by $1_{Delta _{F}}$ and in Remark 4.12, the binary sequence $a_t$ is defined as $a_t=1_{Delta _{F}}(alpha^{t})$ where $alpha$ is primitive over $F_{2^n}$ and $t=0...2^n-2$. Since there is no detailed definition of $1_{Delta _{F}}$, I do not understand what is the meaning of indicator of such a Boolean function. When I searche google, I see the definition of indicator of subsets/subspaces of finite fields.
Thanks for replys.
combinatorics finite-fields boolean-algebra cryptography
asked Mar 20 at 12:53
Kenan DOGANKenan DOGAN
425
$endgroup$
add a comment |
$begingroup$
In the paper "Componentwise APNness, Walsh uniformity of APN functions and cyclic difference sets" by Claude Carlet, it is written that: Let F be any power function on $F_{2^n}$ and $Delta _{F}={F(x)+F(x+1)+1 , xin F_{2^n}}$. In Remark 4.9, the indicator of $Delta _{F}$ is denoted by $1_{Delta _{F}}$ and in Remark 4.12, the binary sequence $a_t$ is defined as $a_t=1_{Delta _{F}}(alpha^{t})$ where $alpha$ is primitive over $F_{2^n}$ and $t=0...2^n-2$. Since there is no detailed definition of $1_{Delta _{F}}$, I do not understand what is the meaning of indicator of such a Boolean function. When I searche google, I see the definition of indicator of subsets/subspaces of finite fields.
Thanks for replys.
combinatorics finite-fields boolean-algebra cryptography
asked Mar 20 at 12:53
Kenan DOGANKenan DOGAN
425
$endgroup$
In the paper "Componentwise APNness, Walsh uniformity of APN functions and cyclic difference sets" by Claude Carlet, it is written that: Let F be any power function on $F_{2^n}$ and $Delta _{F}={F(x)+F(x+1)+1 , xin F_{2^n}}$. In Remark 4.9, the indicator of $Delta _{F}$ is denoted by $1_{Delta _{F}}$ and in Remark 4.12, the binary sequence $a_t$ is defined as $a_t=1_{Delta _{F}}(alpha^{t})$ where $alpha$ is primitive over $F_{2^n}$ and $t=0...2^n-2$. Since there is no detailed definition of $1_{Delta _{F}}$, I do not understand what is the meaning of indicator of such a Boolean function. When I searche google, I see the definition of indicator of subsets/subspaces of finite fields.
Thanks for replys.
combinatorics finite-fields boolean-algebra cryptography
combinatorics finite-fields boolean-algebra cryptography
asked Mar 20 at 12:53
Kenan DOGANKenan DOGAN
425
asked Mar 20 at 12:53
Kenan DOGANKenan DOGAN
425
edited Mar 20 at 19:49
Kenan DOGAN
asked Mar 20 at 12:53
Kenan DOGANKenan DOGAN
425
asked Mar 20 at 12:53
Kenan DOGANKenan DOGAN
425
asked Mar 20 at 12:53
Kenan DOGANKenan DOGAN
425
425
add a comment |
add a comment |
1 Answer
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With regards to your second to last sentence, $Delta_F$ is a subset of $F$, so $1_{Delta_F}$ is an indicator of a subset of a finite field.
$1_{Delta_F}$ is a function from $F$ to ${0,1}$, where $$1_{Delta_F}(x)=begin{cases}1 & xin Delta_F,\0 & xnotinDelta_F.end{cases}$$
answered Mar 20 at 19:51
Mike EarnestMike Earnest
27.1k22152
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1 Answer
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1 Answer
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$begingroup$
With regards to your second to last sentence, $Delta_F$ is a subset of $F$, so $1_{Delta_F}$ is an indicator of a subset of a finite field.
$1_{Delta_F}$ is a function from $F$ to ${0,1}$, where $$1_{Delta_F}(x)=begin{cases}1 & xin Delta_F,\0 & xnotinDelta_F.end{cases}$$
answered Mar 20 at 19:51
Mike EarnestMike Earnest
27.1k22152
$endgroup$
add a comment |
$begingroup$
With regards to your second to last sentence, $Delta_F$ is a subset of $F$, so $1_{Delta_F}$ is an indicator of a subset of a finite field.
$1_{Delta_F}$ is a function from $F$ to ${0,1}$, where $$1_{Delta_F}(x)=begin{cases}1 & xin Delta_F,\0 & xnotinDelta_F.end{cases}$$
answered Mar 20 at 19:51
Mike EarnestMike Earnest
27.1k22152
$endgroup$
add a comment |
$begingroup$
With regards to your second to last sentence, $Delta_F$ is a subset of $F$, so $1_{Delta_F}$ is an indicator of a subset of a finite field.
$1_{Delta_F}$ is a function from $F$ to ${0,1}$, where $$1_{Delta_F}(x)=begin{cases}1 & xin Delta_F,\0 & xnotinDelta_F.end{cases}$$
answered Mar 20 at 19:51
Mike EarnestMike Earnest
27.1k22152
$endgroup$
With regards to your second to last sentence, $Delta_F$ is a subset of $F$, so $1_{Delta_F}$ is an indicator of a subset of a finite field.
$1_{Delta_F}$ is a function from $F$ to ${0,1}$, where $$1_{Delta_F}(x)=begin{cases}1 & xin Delta_F,\0 & xnotinDelta_F.end{cases}$$
answered Mar 20 at 19:51
Mike EarnestMike Earnest
27.1k22152
answered Mar 20 at 19:51
Mike EarnestMike Earnest
27.1k22152
answered Mar 20 at 19:51
Mike EarnestMike Earnest
27.1k22152
answered Mar 20 at 19:51
Mike EarnestMike Earnest
27.1k22152
27.1k22152
add a comment |
add a comment |
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