n-dimensional codes for detecting and correcting multiple errors0
By Morris Rubinoff
Communications of the ACM,
Vol. 4 No. 12, Pages 545-551
10.1145/366853.366878
The paper introduces a new family of codes for detecting and correcting multiple errors in a binary-coded message. The message itself is arranged (conceptually) into a multidimensional rectangular array. The processes of encoding and error detection are based upon parity evaluations along prescribed dimensions of the array. Effectiveness of the codes is increased by introducing a “system check bit”, which is essentially a parity check on the other parity bits. Only three-dimensional codes are discussed in this paper, with parity evaluations along the horizontal, the vertical, and one main diagonal. However, the family of codes is not restricted to three dimensions, as evidenced by the discussion by Minnick and Ashenhurst on a similar multidimensional single-bit selection plan used for another purpose [6]. A four-dimensional code, correcting three and detecting four errors, has been developed; the extension to higher-dimensional codes with greater correction power is straightforward.
The full text of this article is premium content
0 Comments
No entries found
Log in to Read the Full Article
Purchase the Article
Log in
Create a Web Account
If you are an ACM member, Communications subscriber, Digital Library subscriber, or use your institution's subscription, please set up a web account to access premium content and site
features. If you are a SIG member or member of the general public, you may set up a web account to comment on free articles and sign up for email alerts.