# Accession Number:

## AD0677376

# Title:

## SOME ASPECTS OF THE NORM REPRESENTATION FOR ARITHMETIC CHECKING AND CORRECTING CODES,

# Descriptive Note:

# Corporate Author:

## UNIVERSITY OF SOUTHERN CALIFORNIA LOS ANGELES DEPT OF ELECTRICAL ENGINEERING

# Personal Author(s):

# Report Date:

## 1968-06-01

# Pagination or Media Count:

## 121.0

# Abstract:

The properties of the norm representation for integers are extensively investigated. A norm group is defined and the total number of its equivalence classes is found. The number of elements in each equivalence class is computed. The study of the norm representation for integers applies to a development of addition checking and correcting codes. A generalized addition checking and correcting code is proposed, using the concepts of linear spaces. The norm distance between integers is used to define the detecting and correcting capabilities of such codes. Two special cases, the usual AN code and the BN modulo A code, are treated in more detail. The AN code size is found for each value of the constant A. It is shown that the code size of the single error correcting AN code is a monotonically increasing function of A if A is a prime or a power of a prime and 2 or -2 is a primitive root modulo A. Best bounds on the size of AN codes with single error and double error correcting capabilities are found. A BN modulo A code is constructed in such a way that there is no interaction between its information symbol and check symbol. A necessary and sufficient condition for the construction of a single error correcting BN modulo A code is developed. Finally, some new results on optimal single error and multiple error correcting BN modulo A codes are presented. Author

# Descriptors:

# Subject Categories:

- Computer Programming and Software
- Computer Hardware
- Cybernetics