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Multiplication two square- matrices over GF(2)

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0

$begingroup$

Let's say there are two matrices A and B then I want C = A*B mod 2, where A and B compromise of 0 and 1 only. What's the best and optimized algorithm to multiply these matrices. I am able to achieve small optimization by converting addition to bitwise addition and multiplication to xor operation. in the naive method. But still, complexity is O(n^3), where n is the number of rows/column. Strassen's algorithm will not help as the constants have a high cost. Is there any other algorithm?

matrices galois-theory finite-fields

share|cite|improve this question

edited Mar 17 at 12:27

cat

asked Mar 17 at 12:17

catcat

33

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Quick google search: theory.stanford.edu/~yuhch123/files/cbmm.pdf
  $endgroup$
  – Morgan Rodgers
  Mar 17 at 20:51
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  good reference about triangle in a graph.
  $endgroup$
  – loup blanc
  Mar 18 at 16:58
  

  
  
  
  

add a comment | 

0

$begingroup$

Let's say there are two matrices A and B then I want C = A*B mod 2, where A and B compromise of 0 and 1 only. What's the best and optimized algorithm to multiply these matrices. I am able to achieve small optimization by converting addition to bitwise addition and multiplication to xor operation. in the naive method. But still, complexity is O(n^3), where n is the number of rows/column. Strassen's algorithm will not help as the constants have a high cost. Is there any other algorithm?

matrices galois-theory finite-fields

share|cite|improve this question

edited Mar 17 at 12:27

cat

asked Mar 17 at 12:17

catcat

33

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Quick google search: theory.stanford.edu/~yuhch123/files/cbmm.pdf
  $endgroup$
  – Morgan Rodgers
  Mar 17 at 20:51
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  good reference about triangle in a graph.
  $endgroup$
  – loup blanc
  Mar 18 at 16:58
  

  
  
  
  

add a comment | 

$begingroup$

Let's say there are two matrices A and B then I want C = A*B mod 2, where A and B compromise of 0 and 1 only. What's the best and optimized algorithm to multiply these matrices. I am able to achieve small optimization by converting addition to bitwise addition and multiplication to xor operation. in the naive method. But still, complexity is O(n^3), where n is the number of rows/column. Strassen's algorithm will not help as the constants have a high cost. Is there any other algorithm?

matrices galois-theory finite-fields

share|cite|improve this question

edited Mar 17 at 12:27

cat

asked Mar 17 at 12:17

catcat

33

$endgroup$

share|cite|improve this question

edited Mar 17 at 12:27

cat

asked Mar 17 at 12:17

catcat

33

share|cite|improve this question

edited Mar 17 at 12:27

cat

asked Mar 17 at 12:17

catcat

33

asked Mar 17 at 12:17

catcat

33

asked Mar 17 at 12:17

catcat

33