Equidistant frequency permutation arrays and related constant composition codes

IEEE Trans. Inform. Theory

Zhang

et al. 2017

Multiply constant-weight codes (MCWCs) have been recently studied to improve the reliability of certain physically unclonable function response. In this paper, we give combinatorial constructions for MCWCs which yield several new infinite families of optimal MCWCs. Furthermore, we demonstrate that the Johnson type upper bounds of MCWCs are asymptotically tight for fixed weights and distances. Finally, we provide bounds and constructions of two dimensional MCWCs.

Section: B Constructionsmentioning

confidence: 99%

Constructions of Optimal and Near-Optimal Multiply Constant-Weight Codes

IEEE Trans. Inform. Theory

Zhang

et al. 2017

“…Permutation code [16] (q(q + 1), q 2 ) q for prime powers q q 2 q 0 Frequency permutation array [12] ( q(kq [18] (2q − 1, 2q In particular, only six infinite nontrivial families of optimal codes with n > q are known. However, code parameters for these six families are such that their relative narrowband noise error-correcting capability to length ratios diminish to zero as q grows.…”

Section: Theorem 23 the Following Holds (I)mentioning

confidence: 99%

“…Details are provided in Table II. We then prove the lemma by induction on m ≥ 97. Let E = {t : t ≥ 9} \ {10, 14,15,18,20,22,26,30,34,38, 46, 60}. By Theorem 4.8, a TD(7, n) exists for any n ∈ E. If there exists a special GBTD 1 (3, m ) for odd m , 7 ≤ m ≤ 2n + 1, then apply Lemma 7.2 with 3 ≤ g 1 , g 2 ≤ n to obtain a special GBTD 1 (3, m) for odd m, 10n + 7 ≤ m ≤ 14n + 1.…”

Section: Existence Of Gbtd 1 (3 M)mentioning

confidence: 99%

See 1 more Smart Citation

Generalized Balanced Tournament Packings and Optimal Equitable Symbol Weight Codes for Power Line Communications

J of Combinatorial Designs

Ling

et al. 2014

Generalized balanced tournament packings (GBTPs) extend the concept of generalized balanced tournament designs introduced by Lamken and Vanstone (1989). In this paper, we establish the connection between GBTPs and a class of codes called equitable symbol weight codes (ESWCs). The latter were recently demonstrated to optimize the performance against narrowband noise in a general coded modulation scheme for power line communications. By constructing classes of GBTPs, we establish infinite families of optimal ESWCs with code lengths greater than alphabet size and whose narrowband noise error-correcting capability to code length ratios do not diminish to zero as the length grows.

“…Vinck [31] studied this channel and showed that -ary frequency shift keying ( -FSK) modulation, in conjunction with the use of permutation codes, provides a constant power envelope, frequency spreading, and redundancy to correct errors resulting from the harsh noise pattern. This has since resulted in research on frequency permutation arrays (FPAs) and constant composition codes (CCCs) which retain the property of a constant power envelope (see [5]- [16], and [14] for a survey). Every codeword of an FPA or a CCC has the requirement that the frequency of each symbol is fixed by the parameters of the code.…”

Section: Introductionmentioning

confidence: 99%

Estimates on the Size of Symbol Weight Codes

IEEE Trans. Inform. Theory

Purkayastha

2013

The study of codes for powerline communications has garnered much interest over the past decade. Various types of codes such as permutation codes, frequency permutation arrays, and constant composition codes have been proposed over the years. In this paper, we study a type of code called bounded symbol weight codes which was first introduced by Versfeld et al. in 2005, and a related family of codes that we term constant symbol weight codes. We provide new upper and lower bounds on the size of bounded symbol weight and constant symbol weight codes. We also give direct and recursive constructions of codes for certain parameters.