# Accession Number:

## AD0263608

# Title:

## Quaternary Cyclic Codes

# Descriptive Note:

# Corporate Author:

## MASSACHUSETTS INST OF TECH LEXINGTON LINCOLN LAB

# Personal Author(s):

# Report Date:

## 1961-09-13

# Pagination or Media Count:

## 19.0

# Abstract:

Cyclic codes are considered for the quaternary alphabet, the field K GF2 squared. If A is a k,n n odd quaternary group codes - i.e., a k- dimensional subspace of ordered n-tuples of K elements - then A is isomorphic via the Solomon-Mattson polynomials, to a subgroup of the direct product of K with r copies of L. L is the smallest field over K containing the nth roots of unity and r is the number of irreducible factors of x to the n power 1x 1 over K. Let dA,K be the minimum weight of non-zero vectors of A. For p, a prime, and A, a k,p cyclic K code, dA, K greater than or equal to dA,F where dA,F is the Bose-Chaudhuri bound for the corresponding binary cyclic codes of the same order if there is one. Number theoretic methods are introduced to improve the Zierler-Gorenstein lower bound for certain primes p. For p such that 2 has multiplicative order p- 1, there exists p 12, p cyclic codes with dp greater than or equal to 3 is 3 is not a quadratic residue of p, dp greater than or equal to 4 if 3 is a quadratic residue of p, and d greater than or equal to 5 if both 3 and 5 are quadratic residues of p. Author

# Descriptors:

# Subject Categories:

- Theoretical Mathematics