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Peak-to-mean power control in OFDM, Golay complementary sequences and Reed-Muller codes
We present a range of coding schemes for orthogonal frequency division multiplexing (OFDM) transmission at high code rates using binary, quaternary, octary and higher-order modulation. These schemesExpand
Peak-to-mean power control in OFDM, Golay complementary sequences, and Reed-Muller codes
  • J. Davis, J. Jedwab
  • Mathematics, Computer Science
  • IEEE Trans. Inf. Theory
  • 16 August 1998
TLDR
A previously unrecognized connection between Golay complementary sequences and second-order Reed-Muller codes over alphabets Z/sub 2/h is found to give an efficient decoding algorithm involving multiple fast Hadamard transforms. Expand
Peak-to-mean power control and error correction for OFDM transmission using Golay sequences and Reed-Muller codes
TLDR
The scheme solves the notorious problem of power control in OFDM systems by maintaining a peak-to-mean envelope power ratio of at most 3 dB while allowing simple encoding and decoding at high code rates for binary, quaternary or higher-phase signalling together with good error correction. Expand
A Unifying Construction for Difference Sets
  • J. Davis, J. Jedwab
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. A
  • 1 October 1997
We present a recursive construction for difference sets which unifies the Hadamard, McFarland, and Spence parameter families and deals with all abelian groups known to contain such difference sets.Expand
Difference sets in abelian 2-groups
  • J. Davis
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. A
  • 1 July 1991
TLDR
It is shown thatℤ/(2d)×Ω/(2D + 1)×Z/( 2d + 2) both admit difference sets, and this fills in the gap of knowledge between Turyn's exponent condition and Dillon's rank condition. Expand
Amorphic association schemes with negative Latin square-type graphs
  • J. Davis, Qing Xiang
  • Computer Science, Mathematics
  • Finite Fields Their Appl.
  • 21 September 2004
TLDR
This work constructs the first known amorphic association scheme with negative Latin square-type graphs and whose underlying set is a nonelementary abelian 2-group. Expand
Negative Latin Square type Partial Difference Sets in Nonelementary Abelian 2‐Groups
Combining results on quadrics in projective geometries with an algebraic interplay between finite fields and Galois rings, the first known family of partial difference sets with negative Latin squareExpand
Near-complete external difference families
We introduce and explore near-complete external difference families, a partitioning of the nonidentity elements of a group so that each nonidentity element is expressible as a difference of elementsExpand
Linking systems in nonelementary abelian groups
TLDR
This paper defines linking systems, collections of difference sets that correspond to systems of linked designs, and constructs linking systems in a variety of nonelementary abelian groups using Galois rings, partial difference sets, and a product construction. Expand
Construction of relative difference sets in p-groups
  • J. Davis
  • Computer Science, Mathematics
  • Discret. Math.
  • 25 May 1992
TLDR
This paper provides two new constructions of relative difference sets with parameters p -group, and shows that if j is odd, every abelian group of order p j +2 and exponent less than or equal to p ( j +3)/2 has a relative difference set. Expand
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