Geodesic
On key schedule for block ciphers without week keys
Prikladnaya Diskretnaya Matematika. Supplement, no. 9 (2016), pp. 70-73.

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This paper describes the key schedule providing all different round keys for $r$-round symmetric block cipher. The key schedule is implemented by a series connection of automata: an autonomous automaton $A$ generating an output sequence of binary vectors with the period length is not less than $r$, and internally autonomous automaton with permanent memory containing the encryption key of a block cipher. As an example, a linear shift register with a maximum period is considered as the automaton $A$.
Keywords: block cipher, round key, $r$-unrepeatable sequence, $r$-unrepeatable automaton, index of unrepeatability. 
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     author = {V. M. Fomichev},
     title = {On key schedule for block ciphers without week keys},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
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     url = {http://geodesic.mathdoc.fr/item/PDMA_2016_9_a27/}
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V. M. Fomichev. On key schedule for block ciphers without week keys. Prikladnaya Diskretnaya Matematika. Supplement, no. 9 (2016), pp. 70-73. http://geodesic.mathdoc.fr/item/PDMA_2016_9_a27/

[1] Fomichev V. M., Metody diskretnoi matematiki v kriptologii, Dialog-MIFI, M., 2010, 424 pp.

[2] Romanko D. A., Fomichev V. M., “O sposobakh postroeniya kriptograficheskikh generatorov s zadannym pokazatelem bespovtornosti vykhodnykh posledovatelnostei”, Prikladnaya diskretnaya matematika. Prilozhenie, 2016, no. 9, 65–67