A Dual Plotkin Bound for $(T,M,S)$-Nets

2007 ◽  
Vol 53 (1) ◽  
pp. 411-415 ◽  
Author(s):  
William J. Martin ◽  
Terry I. Visentin
Keyword(s):  
Plotkin Bound

On the Construction of Multiply Constant-Weight Codes

2021 ◽  
pp. 1-10
Author(s):  
Jiejing Wen ◽  
Fang-Wei Fu
Keyword(s):  
Constant Weight Codes ◽  
Constant Weight ◽  
Outer Code ◽  
Plotkin Bound ◽  
Johnson Bound

Multiply constant-weight codes (MCWCs) were introduced recently to improve the reliability of certain physically unclonable function response. In this paper, two methods of constructing MCWCs are presented following the concatenation methodology. In other words, MCWCs are constructed by concatenating approximate outer codes and inner codes. Besides, several classes of optimal MCWCs are derived from these methods. In the first method, the outer codes are [Formula: see text]-ary codes and the inner codes are constant-weight codes over [Formula: see text]. Furthermore, if the outer code achieves the Plotkin bound and the inner code achieves Johnson bound, then the resulting MCWC is optimal. In the second method, the outer codes are [Formula: see text]-ary codes and the inner codes are MCWCs. Furthermore, if the outer code achieves the Plotkin bound and the inner code achieves the Johnson bound, then the resulting MCWC is optimal.

ON PLOTKIN-OPTIMAL CODES OVER FINITE FROBENIUS RINGS

2006 ◽  
Vol 05 (06) ◽  
pp. 799-815 ◽  
Author(s):  
MARCUS GREFERATH ◽  
GARY McGUIRE ◽  
MICHAEL E. O'SULLIVAN
Keyword(s):  
Hadamard Matrices ◽  
Interesting Property ◽  
Optimal Codes ◽  
Frobenius Ring ◽  
Frobenius Rings ◽  
Plotkin Bound ◽  
Homogeneous Weight ◽  
Finite Frobenius Rings ◽  
Finite Frobenius Ring ◽  
The Relationship

We study the Plotkin bound for codes over a finite Frobenius ring R equipped with the homogeneous weight. We show that for codes meeting the Plotkin bound, the distribution on R induced by projection onto a coordinate has an interesting property. We present several constructions of codes meeting the Plotkin bound and of Plotkin-optimal codes. We also investigate the relationship between Butson–Hadamard matrices and codes over R meeting the Plotkin bound.

Modified Plotkin bound for unequal error protection codes

2002 ◽  
Vol 38 (18) ◽  
pp. 1041
Author(s):  
Lei Xie ◽  
Huifang Chen ◽  
S. Egami ◽  
Peiliang Qiu
Keyword(s):  
Unequal Error Protection ◽  
Error Protection ◽  
Plotkin Bound

scholarly journals Some Remarks on the Plotkin Bound

10.37236/1746 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Jörn Quistorff
Keyword(s):  
Upper Bound ◽  
Coding Theory ◽  
Minimum Distance ◽  
Binary Codes ◽  
Plotkin Bound ◽  
Hamming Metric ◽  
Lee Metric

In coding theory, Plotkin's upper bound on the maximal cadinality of a code with minimum distance at least $d$ is well known. He presented it for binary codes where Hamming and Lee metric coincide. After a brief discussion of the generalization to $q$-ary codes preserved with the Hamming metric, the application of the Plotkin bound to $q$-ary codes preserved with the Lee metric due to Wyner and Graham is improved.

Two series of equitable symbol weight codes meeting the Plotkin bound

2013 ◽  
Vol 74 (1) ◽  
pp. 15-29 ◽  
Author(s):  
Peipei Dai ◽  
Jianmin Wang ◽  
Jianxing Yin
Keyword(s):  
Plotkin Bound
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