Output details
13 - Electrical and Electronic Engineering, Metallurgy and Materials
University of Plymouth
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Article title
There Is No Binary [35,10,13] Code
Type
D - Journal article
Title of journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Article number
-
Volume number
57
Issue number
9
First page of article
6094
ISSN of journal
0018-9448
Year of publication
2011
Number of additional authors
2
Additional information
We tried to construct a binary code with 35 bits and 10 information bits and a Hamming distance of at least 13 between every codeword. After three fruitless months we came to the conclusion that it was not possible. There are over 10^(75) possible codes, too many to test. The breakthrough came in realising that the code, if it exists, can be shortened to become a (26+x,1+x,13) code. All possibilities of (26+x,1+x,13) codes were constructed, tested and lengthened, one bit at a time, until all codes were eliminated. This novel procedure has been generalised, producing many previously unknown codes.
Interdisciplinary
-
Cross-referral requested
-
Research group
None
Proposed double-weighted
No
Double-weighted statement
-
Reserve for a double-weighted output
No
Non-English
No
English abstract
-
