In his 1961 paper, Marcel Golay showed how the search for pairs of binary sequences of length n with complementary autocorrelation is at worst a 2 3n 2 −6 problem. Andres, in his 1977 master’s thesis, developed an algorithm which reduced this to a 2 n 2 −1 search and investigated lengths up to 58 for existence of pairs. In this paper, we describe refinements to this algorithm, enabling a 2 n 2 ...

We study a construction of the Mathieu group M12 using a game reminiscent of Loyd’s “15-puzzle”. The elements of M12 are realized as permutations on 12 of the 13 points of the finite projective plane of order 3. There is a natural extension to a “pseudogroup” M13 acting on all 13 points, which exhibits a limited form of sextuple transitivity. Another corollary of the construction is a metric, a...

PURPOSE Accurate and efficient guidance of medical devices to procedural targets lies at the heart of interventional procedures. Ultrasound imaging is commonly used for device guidance, but determining the location of the device tip can be challenging. Various methods have been proposed to track medical devices during ultrasound-guided procedures, but widespread clinical adoption has remained e...

For every n divisible by 4, we construct a square matrix H of size n, with coeecients 1, such that H H t nI mod 32. This solves the 32-modular version of the classical Hadamard conjecture. We also determine the set of lengths of 16-modular Golay sequences. 0. Introduction Hadamard matrices can be constructed from various binary sequences, either from Golay complementary sequences, or Williamson...

A split complete weight enumerator in six variables is used to study the colored designs held by codewords of xed composition in Type III codes containing the all one codeword In particular the ternary Golay code contains colored designs We conjecture that every weight class in a Type III code with the all one codeword holds colored designs Introduction Colored designs were introduced in to stu...

As a graduate student, I learned to question assumptions. Michael Barbour taught us to challenge the assumption that we could ever really know the "native" condition of California. Marcel Rejmánek taught me to ask, "Is your invasives problem truly growing over time, or does it just look that way because you are doing a better job of measuring it?" These questions underlie my develop­ ment of mo...

searching through a large volume of data is very critical for companies, scientists, and searching engines applications due to time complexity and memory complexity. In this paper, a new technique of generating FuzzyFind Dictionary for text mining was introduced. We simply mapped the 23 bits of the English alphabet into a FuzzyFind Dictionary or more than 23 bits by using more FuzzyFind Diction...

Golay complementary waveforms can, in theory, yield radar returns of high range resolution with essentially zero sidelobes. In practice, when deployed conventionally, while high signal-to-noise ratios can be achieved for static target detection, significant range sidelobes are generated by target returns of nonzero Doppler causing unreliable detection. We consider signal processing techniques u...

The paper presents the study of synthetic transmit aperture method applying the Golay coded transmission for medical ultrasound imaging. Longer coded excitation allows to increase the total energy of the transmitted signal without increasing the peak pressure. Signal-to-noise ratio and penetration depth are improved maintaining high ultrasound image resolution. In the work the 128-element linea...