Remark on “On DNA Codes” published in Probl. Peredachi Inf., 2005, no. 4

Remark on “On DNA Codes” published in Probl. Peredachi Inf., 2005, no. 4 ISSN 0032-9460, Problems of Information Transmission, 2006, Vol. 42, No. 2, p. 166.  c Pleiades Publishing, Inc., 2006. Original Russian Text  c A.G. D’yachkov, P.A. Vilenkin, I.K. Ismagilov, R.S. Sarbaev, A. Macula, D. Torney, S. White, 2006, published in Problemy Peredachi Informatsii, 2006, Vol. 42, No. 2, p. 109. LETTERS TO THE EDITOR Remark on “On DNA Codes” Published in Probl. Peredachi Inf., 2005, no. 4 A. G. D’yachkov, P. A. Vilenkin, I. K. Ismagilov, R. S. Sarbaev, A. Macula, D.Torney, and S.White DOI: 10.1134/S0032946006020104 In the paper “On DNA Codes” (Probl. Peredachi Inf., 2005, vol. 41, no. 4, pp. 349–367), the assertion of Theorem 4 can be strengthened as follows: There exists a q-ary DNA code of length n, distance D =1, block similarity n − D − 1= n − 2, and size n−1 q + q /2 if n = kq, k =1, 3, 5,... , n−1 m m+k q /2 if q =2 ,n =2 ,k ≥ 1, N = ⎪ n/2+1 q − 1 n−1 q − /2 if n = kq, k =2, 4, 6,... . q − 1 The validity of this statement obviously follows from the arguments of the paper given in the proof of Theorem 4 if one takes into account Lemma 12, which states that a parity-check code does not contain self-reverse-complement sequences for n = kq, k =1, 3, 5,... . February 8, 2006. A.G. D’yachkov, P.A. Vilenkin, I.K. Ismagilov, R.S. Sarbaev, A. Macula, D. Torney, S. White http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

Remark on “On DNA Codes” published in Probl. Peredachi Inf., 2005, no. 4

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Publisher
Nauka/Interperiodica
Copyright
Copyright © 2006 by Pleiades Publishing, Inc.
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946006020104
Publisher site
See Article on Publisher Site

Abstract

ISSN 0032-9460, Problems of Information Transmission, 2006, Vol. 42, No. 2, p. 166.  c Pleiades Publishing, Inc., 2006. Original Russian Text  c A.G. D’yachkov, P.A. Vilenkin, I.K. Ismagilov, R.S. Sarbaev, A. Macula, D. Torney, S. White, 2006, published in Problemy Peredachi Informatsii, 2006, Vol. 42, No. 2, p. 109. LETTERS TO THE EDITOR Remark on “On DNA Codes” Published in Probl. Peredachi Inf., 2005, no. 4 A. G. D’yachkov, P. A. Vilenkin, I. K. Ismagilov, R. S. Sarbaev, A. Macula, D.Torney, and S.White DOI: 10.1134/S0032946006020104 In the paper “On DNA Codes” (Probl. Peredachi Inf., 2005, vol. 41, no. 4, pp. 349–367), the assertion of Theorem 4 can be strengthened as follows: There exists a q-ary DNA code of length n, distance D =1, block similarity n − D − 1= n − 2, and size n−1 q + q /2 if n = kq, k =1, 3, 5,... , n−1 m m+k q /2 if q =2 ,n =2 ,k ≥ 1, N = ⎪ n/2+1 q − 1 n−1 q − /2 if n = kq, k =2, 4, 6,... . q − 1 The validity of this statement obviously follows from the arguments of the paper given in the proof of Theorem 4 if one takes into account Lemma 12, which states that a parity-check code does not contain self-reverse-complement sequences for n = kq, k =1, 3, 5,... . February 8, 2006. A.G. D’yachkov, P.A. Vilenkin, I.K. Ismagilov, R.S. Sarbaev, A. Macula, D. Torney, S. White

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Problems of Information TransmissionSpringer Journals

Published: Jul 7, 2006

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