Engineering topics
Publications and source records attributed to Reichstein, Z..
New theorems aid search for efficient code alphabets. Paper discusses theory of finding largest binary codes 2k bits in length, in which all words differ from each other in at least d places and in which words truncated by ignoring certain subsets of bit positions belong to shorter linear codes.
This note considers codes for computer file transfer protocols when only upper-case ASCII characters are used as control characters. Such a restriction may be necessary to avoid dependence on unique machine features and to promote portability. If ten control functions are needed, a number used in a typical sufficiently rich protocol, we seek a subset of ten upper-case ASCII characters with good distance properties. The control functions form themselves naturally into three groups. Recognizing that only even distances can occur, the need to make the intragroup minimum distances as large as possible, and the number of control characters have distance 2 as small as possible is emphasized. The optimum solution to the above problem is found as well as an assignment that attains the optimum. The codes are essentially unique.
Binary codes with the constraint that the codes restricted to certain subsets of columns must be contained in particular codes of the shorter lengths are considered. In particular, codes of even length 2k, and of minimum distance approximately greater than d, where in 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 are considered. If k = 2n, n odd, and d = 2n, it is proved that the code has at most 8n - 4 codewords, and 8n - 4 is attainable for n = 3. 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 ASCII characters where the Hamming distance between the binary forms of every two different control functions is at least six.
Codes for use in personal computer file transfer as control characters, when only upper-case ASCII can be used to avoid dependence on unique machine features and promote portability. If ten control functions are needed, a number used in at least one protocol, a subset of ten upper-case ASCII characters with good distance properties is sought. The control functions form themselves naturally into three groups, one of two functions (ACK and NAK) and two of four. The aim is to make ACK and NAK as antipodal as possible (distance 6), make the distances within each of the other groups as large as possible (4), and otherwise have as few 2's in the distance table as possible, recognizing that only even distances can occur. The minimum and an assignment that attains the minimum are found. The code is essentially unique. The analogous problem for two groups of three control functions and one group of four is also solved.