ON SELF-DUAL CONVOLUTIONAL CODES OVER RINGS

Abstract

We study the construction of a parity check matrix H(D) ∈ R(D) (n−k)×n

of a rate-k/n convolutional code C over a commutative ring R that sat

isfies the descending chain condition. A (n − k) × n systematic par

ity check matrix H(D) is obtained from a standard generator matrix

G(D) ∈ R(D) k×n of C. If G(D)=(Ik, A) such that n = 2k and

A−1 = −AT , then H(D)=(−AT , Ik) is equivalent to G(D), and con

sequently C is self-dual. New examples of encoders of rate-4/8 self-dual

convolutional codes over the binary field F2 and the integer ring Z4 are

presented.