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 satisfies the descending chain condition. A (n − k) × n systematic parity 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 =2 k and A−1 = −AT, thenH(D)=( −AT,Ik) is equivalent toG(D), and consequently 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.