DocumentCode :
927043
Title :
A new approach to error-correcting codes
Author :
Lempel, Abraham ; Winograd, Shmuel
Volume :
23
Issue :
4
fYear :
1977
fDate :
7/1/1977 12:00:00 AM
Firstpage :
503
Lastpage :
508
Abstract :
A correspondence between linear 
codes and algorithms for computing a system 
of 
bilinear forms is established under which the codelength 
is equal to the multiplicative complexity of the algorithm for computing , and the code distance 
is underbounded by the minimum number of multiplications required to compute any linear combination of the forms in . This hitherto unexplored approach to linear codes holds promise of a better understanding of the structure of existing codes as well as for methods of constructing new codes with prescribed rate and distance.
codes and algorithms for computing a system of bilinear forms is established under which the codelength is equal to the multiplicative complexity of the algorithm for computing , and the code distance is underbounded by the minimum number of multiplications required to compute any linear combination of the forms in . This hitherto unexplored approach to linear codes holds promise of a better understanding of the structure of existing codes as well as for methods of constructing new codes with prescribed rate and distance.Keywords :
Bilinear transformations; Error-correcting codes; Error correction codes; Linear code; Mathematics; Modulation coding; Network address translation; Notice of Violation;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.1977.1055735
Filename :
1055735
Link To Document :
