Abstract
Binary group codes described by Abramson permit the correction of all single errors and all double errors in adjacent digits, with the use of significantly fewer check digits than codes capable of correcting all double-bit errors. This note considers the generalization of Abramson's codes to the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</tex> -nary case, where a symbol alphabet consisting of the digits <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0, 1, \cdots , p - 1</tex> is used for transmission, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</tex> being a prime number. Examples of such <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</tex> -nary codes are given, as well as necessary conditions for their existence. These codes bear the same relation to the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</tex> -nary Golay codes as Abramson's codes do to the familiar Hamming codes. Some as yet unanswered questions are raised, and suggestions for further possible generalizations are given.
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