Computing the Spectrum of a Binary Group Code

The need for reliable data transmission systems has prompted the investigation of various coding techniques which attempt to detect and/or correct transmission errors. Because of the relative ease with which binary codes can be implemented, these codes have received special attention. It is with certain properties of these codes that this paper is concerned. In general, the encoder receives a block of k binary symbols (called a message) from a message source from which it determines (n -- k) binary parity check symbols (called an ending). The message symbols and the ending symbols may be interleaved or transmitted sequentially thus forming a block of length n (called a code vector). Because any * The material presented in this paper formed Appendix II of the dissertation "Coding for Numerical Data Transmission" submitted by the author to The Johns Hopkins University in conformity with the requirements for the degree Doctor of Philosophy. 441 442 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1966