scholarly journals On the complete pivoting conjecture for a hadamard matrix of order 12

2019 ◽  
Vol 38 (3) ◽  
pp. 181-187
Author(s):  
Alan Edelman ◽  
Walters Mascarenhas
Keyword(s):  
Hadamard Matrix ◽  
Complete Pivoting

scholarly journals On the complete pivoting conjecture for a hadamard matrix of order 12

1995 ◽  
Vol 38 (3) ◽  
pp. 181-187 ◽  
Author(s):  
Alan Edelman ◽  
Walters Mascarenhas
Keyword(s):  
Hadamard Matrix ◽  
Complete Pivoting

scholarly journals An infinite family of Williamson matrices

1977 ◽  
Vol 24 (2) ◽  
pp. 252-256 ◽  
Author(s):  
Edward Spence
Keyword(s):  
Prime Power ◽  
Hadamard Matrix ◽  
Infinite Family ◽  
Williamson Matrices

AbstractIn this paper the following result is proved. Suppose there exists a C-matrix of order n + 1. Then if n≡1 (mod 4) there exists a Hadamard matrix of order 2nr(n + 1), while if n≡3 (mod 4) there exists a Hadamard matrix of order nr(n + 1) for all r ≧0. If n≡1 (mod 4) is a prime power, the method is adapted to prove the existence of a Hadamard matrix of the Williamson type, of order 2nr(n + 1), for all r ≧0.

scholarly journals A skew-Hadamard matrix of order 92

1971 ◽  
Vol 5 (2) ◽  
pp. 203-204 ◽  
Author(s):  
Jennifer Wallis
Keyword(s):  
Hadamard Matrix

There is a skew-Hadamard matrix of order 92.Previously the smallest order for which a skew-Hadamard matrix was not known was 92. We construct such a matrix below. The orders < 200 which are now undecided are 100, 116, 148, 156, 172, 188, 196; see [2], [3]. The existence of any Hadamard matrix of order 92 was unknown until 1962 [1].

A Hadamard Matrix

1997 ◽  
pp. 3-3
Author(s):  
R. K. Rao Yarlagadda ◽  
John E. Hershey
Keyword(s):  
Hadamard Matrix

scholarly journals THE WEIGHT HIERARCHY OF HADAMARD CODES

2019 ◽  
pp. 797
Author(s):  
Farzaneh Farhang Baftani ◽  
Hamid Reza Maimani
Keyword(s):  
Binary Code ◽  
Hadamard Matrix ◽  
Hamming Weight ◽  
Generalized Hamming Weight ◽  
Hadamard Codes ◽  
Hadamard Code ◽  
Weight Hierarchy

The support of an $(n, M, d)$ binary code  $C$ over the set $\mathbf{A}=\{0,1\}$ is the set of all coordinate positions $i$, such  that  at  least two codewords  have distinct entry  in  coordinate $i$.  The  $r$th  generalized  Hamming  weight  $d_r(C)$,  $1\leq r\leq 1+log_2n+1$,  of  $C$  is  defined  as  the minimum  of  the  cardinalities  of  the  supports  of  all subset  of  $C$ of cardinality $2^{r-1}+1$.  The  sequence $(d_1(C), d_2(C), \ldots, d_k(C))$ is called the Hamming weight hierarchy (HWH) of $C$. In this paper we obtain HWH for $(2^k-1, 2^k, 2^{k-1}$ binary Hadamard code corresponding to Sylvester Hadamard matrix $H_{2^k}$ and we show that    $$d_r=2^{k-r} (2^r -1).$$ Also we compute the HWH of all $(4n-1, 4n, 2n)$ Hadamard code for $2\leq n\leq 8$.

scholarly journals Construction of Error-Correction Code Application by Applying Finite Field and Hadamard Matrix Theory

Jurnal MIPA ◽  
2012 ◽  
Vol 1 (1) ◽  
pp. 45
Author(s):  
Robinson Pongoh ◽  
Benny Pinontoan ◽  
Winsy Weku
Keyword(s):  
Finite Field ◽  
Error Correction ◽  
Matrix Theory ◽  
Hadamard Matrix ◽  
Divide And Conquer ◽  
Application Development ◽  
Error Correction Code ◽  
Rapid Application Development

Dalam dunia elektronik dan digital, informasi dapat dengan mudahditransfer melalui saluran komunikasi. Pada data yang ditransfer galatdapat muncul dikarenakan oleh berbagai akibat. Untuk menghindarimasalah ini diperlukan kode perbaikan-galat bersama aplikasinya. Konsepdari kode perbaikan-galat adalah untuk menambahkan bit-tambahanpada data agar disaat pengiriman, data tersebut lebih kuat dalammenghadapi gangguan yang hadir di saluran komunikasi. Random ParityCode (RPC) yang dikemukakan oleh Hershey dan Tiemann (1996) adalahsalah satu dari kode yang dimaksud. Artikel ini menunjukan pembuatanaplikasi kode perbaikan-galat yang dibuat berdasarkan konsep RPCdengan bantuan teori Lapangan Terbatas dan Matriks Hadamard. Aplikasidibuat menggunakan Metode Rapid Application Development (RAD).Aplikasi dihasilkan dalam bentuk perangkat lunak komputer. Perangkatlunak tersebut menjadi lebih efisien dengan menerapkan konsepalgoritma “Divide and Conquer”.

Implementation of Orthogonal Codes Using MZI

2020 ◽  
Vol 12 (3) ◽  
pp. 159-167
Author(s):  
Supriti Samanta ◽  
Goutam K. Maity ◽  
Subhadipta Mukhopadhyay
Keyword(s):  
Hadamard Matrix ◽  
Extinction Ratio ◽  
Optical Amplifier ◽  
Zehnder Interferometer ◽  
Nonlinear Phase ◽  
Orthogonal Codes ◽  
Hadamard Codes ◽  
Code Division Multiple ◽  
And Control ◽  
Mach Zehnder Interferometer

Background: In Code Division Multiple Access (CDMA)/Multi-Carrier CDMA (MCCDMA), Walsh-Hadamard codes are widely used for its orthogonal characteristics, and hence, it leads to good contextual connection property. These orthogonal codes are important because of their various significant applications. Objective: To use the Mach–Zehnder Interferometer (MZI) for all-optical Walsh-Hadamard codes is implemented in this present paper. Method: The Mach–Zehnder Interferometer (MZI) is considered for the Tree architecture of Semiconductor Optical Amplifier (SOA). The second-ordered Hadamard and the inverse Hadamard matrix are constructed using SOA-MZIs. Higher-order Hadamard matrix (H4) formed by the process of Kronecker product with lower-order Hadamard matrix (H2) is also analyzed and constructed. Results: To experimentally get the result from these schemes, some design issues e,g Time delay, nonlinear phase modulation, extinction ratio, and synchronization of signals are the important issues. Lasers of wavelength 1552 nm and 1534 nm can be used as input and control signals, respectively. As the whole system is digital, intensity losses due to couplers in the interconnecting stage may not create many problems in producing the desired optical bits at the output. The simulation results were obtained by Matlab-9. Here, Hadamard H2 (2×2) matrix output beam intensity (I ≈ 108 w.m-2) for different values of inputs. Conclusion: Implementation of Walsh-Hadamard codes using MZI is explored in this paper, and experimental results show the better performance of the proposed scheme compared to recently reported methods using electronic circuits regarding the issues of versatility, reconfigurability, and compactness. The design can be used and extended for diverse applications for which Walsh-Hadamard codes are required.

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