PERFECT DOUBLE HAMMING-ERROR-CORRECTING CODES ON Q-SYMBOLS,
Ronald Alter · Defense Technical Information Center (DTIC) · 1969
All previously published results in this area are stated. This includes the cases Q = 2, 3, 4, 5, and 6 and the author's results for the case Q = 7. The theorem, that for any Q there exist at most a finite number of perfect double Hamming-error-correcting codes on Q-symbols, is proven. The author's method, the use of continued fractions for solving Diophantine equations, is generalized and extended so that results for larger values of Q are in fact attained. In addition, the difficulties which arise in applying this method for all values of Q are discussed. (Author)