Hong-Yup Song

In this correspondence, it is shown that Legendre sequences of period p can be explicitly represented using the trace function defined on the finite field with 2/sup n/ elements, whenever p=2/sup n/-1 is prime for some n/spl ges/3.

We classify some p/sup k/-ary (p prime, k integer) generalized m-sequences and generalized Gordon-Mills-Welch (GMW) sequences of period p/sup 2k/-1 over a residue class ring R=GF(p)[/spl xi/]/(/spl xi//sup k/) having optimal partial Hamming autocorrelation properties. In frequency hopping (FH) spread-spectrum systems, these sequences are useful for synchronizing process. Suppose, for example, that a transmitting p/sup k/-ary FH patterns of period p/sup 2k/-1 are correlated at a receiver. Usually

The main conjecture of this article is the following: if a cyclic (v=4n-1, k=2n-1, /spl lambda/=n-1) Hadamard difference set exists, the the value of v must be either a prime, or a product of "twin primes," or one less than a power of 2. Six cases, v=399, 495, 627, 651, 783, and 975, which were once listed as the possible exceptions for v<1000, are now fully investigated, and all the cases of v<10000 are now verified relative to this conjecture, with at most 17 possible exceptions.< <ETX xmlns:m

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this correspondence, we present a connection between designing low-correlation zone (LCZ) sequences and the results of correlation of sequences with subfield decompositions presented in a recent book by the first two authors. This results in LCZ signal sets with huge sizes over three different alphabetic sets: finite field of size <emphasis><formula formulatype="inline"><tex>$q$</tex></formula></e

Variable-to-check residual belief propagation for LDPC decoding for faster convergence, better error performance and lower complexity is proposed. It is similar to residual belief propagation (RBP) that was recently applied to LDPC decoding by Vila Casado et al. because it is also a dynamic scheduling belief propagation using residuals, but it is different because the residuals are computed from a variable-to-check message. Simulation shows that it outperforms with only a maximum of eight iterat

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) Sigma /sub d mod n/ mu (d)q/sup 1+k/d/, where mu (d) is the Mobius 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 mod E"

Three constructions for n-dimensional regular simplex codes /spl alpha//sub i/, 0/spl les/i/spl les/n, are proposed, two of which have the property that /spl alpha//sub i/ for 1/spl les/i/spl les/n is a cyclic shift of /spl alpha//sub 1/. The first method is shown to work for all the positive integers n=1,2,... using only three real values. It turns out that these values are rational whenever n+1 is a square of some integer. Whenever a (v,k,/spl lambda/) cyclic (or Abelian) difference set exists

Abstract In this paper, an algebraic construction of regular QC‐LDPC codes by using the modular multiplication table mod P and Golomb rulers are proposed. It is proved that the proposed QC‐LDPC codes based on a Golomb ruler of length L have girth at least 8 if . The error performance of the proposed QC‐LDPC codes are simulated with various Golomb rulers. The proposed codes of length around 300 from the optimal 6‐mark Golomb ruler have an additional coding gain of at least 0.1 dB over 5G NR LDPC

Abstract Feedback Shift Register (FSR) sequences have been successfully implemented in many communication systems for their randomness properties and ease of implementation. These include ranging and navigation systems, spread spectrum communication systems, CDMA mobile communication systems, and crypto systems such as streamciphers. This article gives a brief overview of FSR sequences, both linear and non‐linear. Two conditions on the connection logic of FSRs for better output sequences are des

Considering the availability of the global navigation satellite system (GNSS) signals and the increase in its data rate in the future, this paper proposes some new Reed-Solomon coded (RS-coded) orthogonal modulation schemes using the Hadamard codes, as an alternative to the RS-coded code-shift-keying (CSK) modulation in the Quasi-Zenith Satellite System L-band experimental (QZSS-LEX) signals. The simulation result of the proposed schemes shows that, though the frame size and hence the data rate