Abstract
Picking up exactly one member from each of the nonperiodic cyclic equivalence classes of an (n, k + 1) Reed-Solomon code E over GF(q) gives a code, E”, which has bounded Hamming correlation values and the self-synchronizing property. The exact size of E” is shown to be 1/n∑dn μ(d)q1+[k/d], where µ(d) is the Möbius function, [x] is the integer part of x, and the summation is over all the divisors d of n = q ~ 1. A construction for a subset V of E is given to prove that |E“| ≥ |V| = (qk+1-qk+1-N)/(q — 1) where N is the number of integers from 1 to k which are relatively prime to q —1. A necessary and sufficient condition for |E“| = |V| is proved and some special cases are presented with examples. Furthermore, for all possible values of q2, a number B(q) is determined such that |E“| = |V| for 1 ≤k ≤ B(q) and “||V| for kB(q).
| Original language | English |
|---|---|
| Pages (from-to) | 1431-1434 |
| Number of pages | 4 |
| Journal | IEEE Transactions on Information Theory |
| Volume | 39 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 1993 Jul |
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All Science Journal Classification (ASJC) codes
- Information Systems
- Computer Science Applications
- Library and Information Sciences
Cite this
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On the Nonperiodic Cyclic Equivalence Classes of Reed-Solomon Codes. / Song, H. Y.; Reed, I. S.; Golomb, S. W.
In: IEEE Transactions on Information Theory, Vol. 39, No. 4, 07.1993, p. 1431-1434.Research output: Contribution to journal › Article
TY - JOUR
T1 - On the Nonperiodic Cyclic Equivalence Classes of Reed-Solomon Codes
AU - Song, H. Y.
AU - Reed, I. S.
AU - Golomb, S. W.
PY - 1993/7
Y1 - 1993/7
N2 - Picking up exactly one member from each of the nonperiodic cyclic equivalence classes of an (n, k + 1) Reed-Solomon code E over GF(q) gives a code, E”, which has bounded Hamming correlation values and the self-synchronizing property. The exact size of E” is shown to be 1/n∑dn μ(d)q1+[k/d], where µ(d) is the Möbius function, [x] is the integer part of x, and the summation is over all the divisors d of n = q ~ 1. A construction for a subset V of E is given to prove that |E“| ≥ |V| = (qk+1-qk+1-N)/(q — 1) where N is the number of integers from 1 to k which are relatively prime to q —1. A necessary and sufficient condition for |E“| = |V| is proved and some special cases are presented with examples. Furthermore, for all possible values of q2, a number B(q) is determined such that |E“| = |V| for 1 ≤k ≤ B(q) and “||V| for kB(q).
AB - Picking up exactly one member from each of the nonperiodic cyclic equivalence classes of an (n, k + 1) Reed-Solomon code E over GF(q) gives a code, E”, which has bounded Hamming correlation values and the self-synchronizing property. The exact size of E” is shown to be 1/n∑dn μ(d)q1+[k/d], where µ(d) is the Möbius function, [x] is the integer part of x, and the summation is over all the divisors d of n = q ~ 1. A construction for a subset V of E is given to prove that |E“| ≥ |V| = (qk+1-qk+1-N)/(q — 1) where N is the number of integers from 1 to k which are relatively prime to q —1. A necessary and sufficient condition for |E“| = |V| is proved and some special cases are presented with examples. Furthermore, for all possible values of q2, a number B(q) is determined such that |E“| = |V| for 1 ≤k ≤ B(q) and “||V| for kB(q).
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UR - http://www.scopus.com/inward/citedby.url?scp=0027799665&partnerID=8YFLogxK
U2 - 10.1109/18.243465
DO - 10.1109/18.243465
M3 - Article
AN - SCOPUS:0027799665
VL - 39
SP - 1431
EP - 1434
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
SN - 0018-9448
IS - 4
ER -