Minimum distance of a code Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Permutation of the columns of an extended binary Hamming codeMinimum distance of the linear code $0,1$Binary BCH code with given distance and rateConstructing a Cyclic code of length p-1 with minimal distance d<=p-1 if p is primeMost efficient method for constructing a linear code with large minimum distanceParity check Matrix for Plotkin construction of linear codesFinding the minimum distance $d=d(C)$ of $C$Does the definition of linear code implies that $E(c_1 + c_2) = E(c_1) + E(c_2)$ for encoding function $E$?Demonstration min(LD columns) is minimum distanceWhat are linear codes having minimum distance 2 used for?
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Minimum distance of a code
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Permutation of the columns of an extended binary Hamming codeMinimum distance of the linear code $0,1$Binary BCH code with given distance and rateConstructing a Cyclic code of length p-1 with minimal distance d<=p-1 if p is primeMost efficient method for constructing a linear code with large minimum distanceParity check Matrix for Plotkin construction of linear codesFinding the minimum distance $d=d(C)$ of $C$Does the definition of linear code implies that $E(c_1 + c_2) = E(c_1) + E(c_2)$ for encoding function $E$?Demonstration min(LD columns) is minimum distanceWhat are linear codes having minimum distance 2 used for?
$begingroup$
Is there a way to compute minimum distance of a code given a systematic parity check matrix? I know that min dist is smallest number $d$ such that there exists $d$ linearly dependant columns. I am looking in particular to find minimum distance of binary (codes over $mathbbF_2^l$) quasi-cyclic of rate q/q+1. Parity check matrix for such codes have a structure
$H=[I|C_1|C_2|...|C_m]$ where each $C_¡$ is a from class of circulant matrices. It may be useful that one can treat these codes as modules.
Or even if there are any approximate algoruihms for this ?
modules coding-theory
asked Apr 2 at 8:14
RootRoot
53
$endgroup$
add a comment |
$begingroup$
Is there a way to compute minimum distance of a code given a systematic parity check matrix? I know that min dist is smallest number $d$ such that there exists $d$ linearly dependant columns. I am looking in particular to find minimum distance of binary (codes over $mathbbF_2^l$) quasi-cyclic of rate q/q+1. Parity check matrix for such codes have a structure
$H=[I|C_1|C_2|...|C_m]$ where each $C_¡$ is a from class of circulant matrices. It may be useful that one can treat these codes as modules.
Or even if there are any approximate algoruihms for this ?
modules coding-theory
asked Apr 2 at 8:14
RootRoot
53
$endgroup$
2
$begingroup$
In coding theory written in English, it is almost universally true that $k$ denotes the number of information symbols and $d$ or $d_min$ the minimum distance of the code. Please don't introduce a new nonstandard meaning for $k$.
$endgroup$
– Dilip Sarwate
Apr 2 at 13:43
add a comment |
$begingroup$
Is there a way to compute minimum distance of a code given a systematic parity check matrix? I know that min dist is smallest number $d$ such that there exists $d$ linearly dependant columns. I am looking in particular to find minimum distance of binary (codes over $mathbbF_2^l$) quasi-cyclic of rate q/q+1. Parity check matrix for such codes have a structure
$H=[I|C_1|C_2|...|C_m]$ where each $C_¡$ is a from class of circulant matrices. It may be useful that one can treat these codes as modules.
Or even if there are any approximate algoruihms for this ?
modules coding-theory
asked Apr 2 at 8:14
RootRoot
53
$endgroup$
Is there a way to compute minimum distance of a code given a systematic parity check matrix? I know that min dist is smallest number $d$ such that there exists $d$ linearly dependant columns. I am looking in particular to find minimum distance of binary (codes over $mathbbF_2^l$) quasi-cyclic of rate q/q+1. Parity check matrix for such codes have a structure
$H=[I|C_1|C_2|...|C_m]$ where each $C_¡$ is a from class of circulant matrices. It may be useful that one can treat these codes as modules.
Or even if there are any approximate algoruihms for this ?
modules coding-theory
modules coding-theory
asked Apr 2 at 8:14
RootRoot
53
asked Apr 2 at 8:14
RootRoot
53
edited Apr 3 at 6:32
Root
asked Apr 2 at 8:14
RootRoot
53
asked Apr 2 at 8:14
RootRoot
53
asked Apr 2 at 8:14
RootRoot
53
53
2
$begingroup$
In coding theory written in English, it is almost universally true that $k$ denotes the number of information symbols and $d$ or $d_min$ the minimum distance of the code. Please don't introduce a new nonstandard meaning for $k$.
$endgroup$
– Dilip Sarwate
Apr 2 at 13:43
add a comment |
2
$begingroup$
In coding theory written in English, it is almost universally true that $k$ denotes the number of information symbols and $d$ or $d_min$ the minimum distance of the code. Please don't introduce a new nonstandard meaning for $k$.
$endgroup$
– Dilip Sarwate
Apr 2 at 13:43
2
2
$begingroup$
In coding theory written in English, it is almost universally true that $k$ denotes the number of information symbols and $d$ or $d_min$ the minimum distance of the code. Please don't introduce a new nonstandard meaning for $k$.
$endgroup$
– Dilip Sarwate
Apr 2 at 13:43
$begingroup$
In coding theory written in English, it is almost universally true that $k$ denotes the number of information symbols and $d$ or $d_min$ the minimum distance of the code. Please don't introduce a new nonstandard meaning for $k$.
$endgroup$
– Dilip Sarwate
Apr 2 at 13:43
add a comment |
0
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$begingroup$
In coding theory written in English, it is almost universally true that $k$ denotes the number of information symbols and $d$ or $d_min$ the minimum distance of the code. Please don't introduce a new nonstandard meaning for $k$.
$endgroup$
– Dilip Sarwate
Apr 2 at 13:43