In this paper, we propose a new encoding algorithm applicable to any linear codes over arbitrary finite field whose computational complexity is O(w(H)) where w(H) denotes the number of non-zero elements in a parity check matrix H of a code. The proposed algorithm is essentially equivalent to the linear time encoding algorithm presented by Lu et al. when the maximum column weight δ∗ of H is less than or equal to 3, and is regarded as a natural generalization of the algorithm when δ∗ > 3. Moreover, the proposed algorithm can encode any linear codes defined by sparse parity check matrices, such as LDPC codes, with O(n) complexity where n denotes the code length.
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