ON SELF-DUAL CONVOLUTIONAL CODES OVER RINGS

Herbert S. Palines, Virgilio P. Sison

Abstract


We study the construction of a parity check matrix H(D) \in R(D)^{(n?k)}
of a rate-k/n convolutional code C over a commutative ring R that satisfies the descending chain condition. A (n?k) systematic parity check matrix H(D) is obtained from a standard generator matrix
G(D) \in R(D)^{k} of C. If G(D)=(Ik,A) such that n=2k and A^{?1}=?A^T, then H(D)=(?A^T,Ik) is equivalent to G(D), and consequentlyCis 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.

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