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