Minimum-distance Problems in Protocol Design

Abstract

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.