Citation
Abstract
This article considers binary codes with the constraint that the codes restricted to certain subsets of columns must be contained in particular codes of the shorter lengths. In particular, we consider codes of even length 2k, and of minimum distance > d, where the code obtained by restricting to the first k positions has even weight and at the same time the code obtained by restricting to the last k positions also has even weight. If k = 2n, n odd, and d = 2n, we prove that the code has at most 8n - 4 codewords, and &n - 4 is attainable for n = 3. This yields 20 binary words of length 12, distance 7 6, where the number of 1’s in the first six and the last six positions is even for every codeword in the code. This permits a file-transfer protocol control function assignment for personal computers to be chosen for 20 control functions using essentially just pairs of upper-case alphabetic ASCH characters where the Hamming distance between the binary forms of every two different control functions is at least six.
Details
- Volume
- 42-80
- Published
- February 15, 1985
- Pages
- 236–247
- File Size
- 574.2 KB