Title :
m-adic residue codes
Author_Institution :
Dept. of Math. & Comput. Sci., Marymount Univ., Arlington, VA, USA
fDate :
3/1/1992 12:00:00 AM
Abstract :
The m-adic residue codes are investigated and are found to have many of the strong properties of the quadratic residue codes. A subgroup of the automorphism group and restrictions on the form of the idempotents of the m-adic residue codes are given. It is shown that some m-adic residue codes are self-orthogonal and the duals of some m-adic residue codes are their complements. Bounds on the minimum of the weights of the odd-like vectors in the odd-like codes are given. At some lengths, m-adic residue codes exist for several values of m. Containment relationships between these codes are demonstrated which show that, when m is even, m-adic residue codes inherit properties of quadratic residue codes. A table is included that contains minimum weights of the binary m-adic residue codes of lengths less than or equal to 127.<>
Keywords :
error correction codes; automorphism group; binary codes; containment relationships; duals; error correction codes; idempotents; m-adic residue codes; minimum weights; odd-like codes; odd-like vectors; quadratic residue codes; self-orthogonal codes; Binary codes; Error correction codes; Information theory; Mathematics; Polynomials; Terminology;
Journal_Title :
Information Theory, IEEE Transactions on
