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Two convolutional-code construction schemes that utilize block codes are given. In the first method the generators of a self-orthogonal convolutional code (SOCC) are expanded. The generators of a block code whose block length is longer than that of the SOCC code replace the nonzero blocks of the convolutional code. The zero blocks are extended to the longer block length. There results a convolutional code whose blocks are self-orthogonal and which has a lower transmission rate. In the second scheme the parity constraints of an SOCC are expanded. The parity constraints of a block code replace some of the individual nonzero elements of the SOCC parity-check matrix, so that the convolutional code rate is greater than the block code rate. The resulting codes retain the SOCC advantages of simple implementation and limited error propagation. Both the encoding and the decoding can be based on the underlying block code. If a block code is majority decodable, then the resulting "hybrid" codes are majority decodable. Optimum majority-decodable block codes with up to five information bits per block are given, and from these codes several majority-decodable convolutional codes that are "optimum" with respect to the proposed construction are obtained.