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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Perfect multiple error-correcting arithmetic codes
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by Daniel M. Gordon PDF
Math. Comp. 49 (1987), 621-633 Request permission


An arithmetic code is a subgroup of ${{\mathbf {Z}}_{{r^n} \pm 1}}$, with the arithmetic distance $d(x,y) = {\min _t}x - y \equiv \Sigma _{i = 1}^t{c_i}{r^{n(i)}}\;(\bmod {r^n} \pm 1)$, for $|{c_i}| < r$, $n(i) \geqslant 0$ for $1 \leqslant i \leqslant t$. A perfect e-error-correcting code is one from which all $x \in {{\mathbf {Z}}_{{r^n} \pm 1}}$, are within distance e of exactly one codeword. Necessary and sufficient (assuming the Generalized Riemann Hypothesis) conditions for the existence of infinitely many perfect single error-correcting codes for a given r are known. In this paper some conditions for the existence of perfect multiple error-correcting codes are given, as well as the results of a computer search for examples.
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Math. Comp. 49 (1987), 621-633
  • MSC: Primary 11T71; Secondary 94B40
  • DOI:
  • MathSciNet review: 906195