New family of single-error correcting codes
- 1 November 1970
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 16 (6) , 717-719
- https://doi.org/10.1109/tit.1970.1054540
Abstract
A construction is given that combines an(n, M_1, d_1)code with an(n, M_2, d_2 = [\frac{1}{2}(d_1 + 1)])code to form a(2n, M_1 M_2, d_1)code. This is used to construct a new family of nongroup single-error correcting codes of all lengthsnfrom2^mto 3 ·2^{m-1} - 1, for everym \geq 3. These codes have more codewords than any group code of the same length and minimum distance. A number of other nongroup codes are also obtained. Examples of the new codes are (16,2560,3) and (16,36,7) codes, both having more codewords than any comparable group code.Keywords
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