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Existence of time-invariant convolutional codes with transmission rate $$2/c$$ for $$c \geq{}4$$ attaining the Costello bound. (English. Russian original) Zbl 0744.94011
Probl. Inf. Transm. 27, No. 3, 199-211 (1991); translation from Probl. Peredachi Inf. 27, No. 3, 16-29 (1991).
A lower bound for the weights of codewords generated by time-invariant $$(c,2)$$-convolutional encoders $$(c\geq 4)$$ is derived. From this lower bound it follows that there exist rate $$2/c$$ convolutional codes whose free distance $$d_{free}$$ asymptotically meets the Costello-bound.
Reviewer: L.Staiger (Siegen)
##### MSC:
 94B10 Convolutional codes 94B65 Bounds on codes
##### Keywords:
free distance; lower bound; convolutional codes; Costello- bound