On a class of error correcting binary group codes
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A general method of constructing error correcting binary group codes is obtained and an example is worked out to illustrate the method of construction.Abstract:
A general method of constructing error correcting binary group codes is obtained. A binary group code with n places, k of which are information places is called an (n,k) code. An explicit method of constructing t-error correcting (n,k) codes is given for n = 2m−1 and k = 2m−1−R(m,t) ≧ 2m−1−mt where R(m,t) is a function of m and t which cannot exceed mt. An example is worked out to illustrate the method of construction.read more
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Error detecting and error correcting codes
TL;DR: The author was led to the study given in this paper from a consideration of large scale computing machines in which a large number of operations must be performed without a single error in the end result.
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A class of binary signaling alphabets
TL;DR: A class of binary signaling alphabets called “group alphABets” is described, which are generalizations of Hamming's error correcting codes and possess the following special features: all letters are treated alike in transmission; the encoding is simple to instrument; maximum likelihood detection is relatively simple to Instrument.
Journal ArticleDOI
Multiple error correction by means of parity checks
TL;DR: It is shown that the characteristics of a n-place binary parity check code have the essential property that any subset of 2e of them are linearly independent.