Transform domain characterization of cyclic codes overZ m

1994 ◽  
Vol 5 (5) ◽  
pp. 261-275 ◽  
Author(s):  
B. Sundar Rajan ◽  
M. U. Siddiqi
Keyword(s):  
Cyclic Codes ◽  
Transform Domain

scholarly journals Self-Dual Abelian Codes in Some Nonprincipal Ideal Group Algebras

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Parinyawat Choosuwan ◽  
Somphong Jitman ◽  
Patanee Udomkavanich
Keyword(s):  
Cyclic Codes ◽  
Group Algebras ◽  
Dual Codes ◽  
Complete Enumeration ◽  
Odd Order ◽  
Abelian Codes ◽  
Positive Integers ◽  
Ideal Group ◽  
Suitable Product

The main focus of this paper is the complete enumeration of self-dual abelian codes in nonprincipal ideal group algebrasF2k[A×Z2×Z2s]with respect to both the Euclidean and Hermitian inner products, wherekandsare positive integers andAis an abelian group of odd order. Based on the well-known characterization of Euclidean and Hermitian self-dual abelian codes, we show that such enumeration can be obtained in terms of a suitable product of the number of cyclic codes, the number of Euclidean self-dual cyclic codes, and the number of Hermitian self-dual cyclic codes of length2sover some Galois extensions of the ringF2k+uF2k, whereu2=0. Subsequently, general results on the characterization and enumeration of cyclic codes and self-dual codes of lengthpsoverFpk+uFpkare given. Combining these results, the complete enumeration of self-dual abelian codes inF2k[A×Z2×Z2s]is therefore obtained.

scholarly journals Skew cyclic codes over 𝔽4R

2020 ◽  
pp. 2250065
Author(s):  
Nasreddine Benbelkacem ◽  
Martianus Frederic Ezerman ◽  
Taher Abualrub ◽  
Nuh Aydin ◽  
Aicha Batoul
Keyword(s):  
Error Control ◽  
Cyclic Codes ◽  
Gray Map ◽  
Inner Product ◽  
Algebraic Structures ◽  
Error Control Codes ◽  
Dna Codes ◽  
Natural Connection ◽  
Skew Cyclic Codes

This paper considers a new alphabet set, which is a ring that we call [Formula: see text], to construct linear error-control codes. Skew cyclic codes over this ring are then investigated in details. We define a nondegenerate inner product and provide a criteria to test for self-orthogonality. Results on the algebraic structures lead us to characterize [Formula: see text]-skew cyclic codes. Interesting connections between the image of such codes under the Gray map to linear cyclic and skew-cyclic codes over [Formula: see text] are shown. These allow us to learn about the relative dimension and distance profile of the resulting codes. Our setup provides a natural connection to DNA codes where additional biomolecular constraints must be incorporated into the design. We present a characterization of [Formula: see text]-skew cyclic codes which are reversible complement.

Transform domain characterization of abelian codes

1992 ◽  
Vol 38 (6) ◽  
pp. 1817-1821 ◽  
Author(s):  
B.S. Rajan ◽  
M.U. Siddiqi
Keyword(s):  
Transform Domain ◽  
Abelian Codes

A Characterization of the q-Ary Images of qm-Ary Cyclic Codes

1993 ◽  
pp. 97-106
Author(s):  
G. E. Séguin ◽  
I. Woungang
Keyword(s):  
Cyclic Codes

scholarly journals DFT Domain Characterization of Quasi-Cyclic Codes

2003 ◽  
Vol 13 (6) ◽  
pp. 453-474 ◽  
Author(s):  
Bikash Kumar Dey ◽  
B. Sundar Rajan
Keyword(s):  
Cyclic Codes ◽  
Quasi Cyclic Codes

scholarly journals COMPUTATIONLESS PALM-PRINT VERIFICATION USING WAVELET ORIENTED ZERO-CROSSING SIGNATURE

2022 ◽  
Vol 23 (1) ◽  
pp. 222-232
Author(s):  
Jitendra Chaudhari ◽  
Hiren Mewada ◽  
Amit Patel ◽  
Keyur Mahant ◽  
Alpesh Vala
Keyword(s):  
Euclidean Distance ◽  
Vertical Direction ◽  
Texture Features ◽  
Discrete Wavelet ◽  
Transform Domain ◽  
Recognition Time ◽  
Zero Crossing ◽  
Palm Print ◽  
Best Fit

Palmprints can be characterized by their texture and the patterns of that texture dominate in a vertical direction. Therefore, the energy of the coefficients in the transform domain is more concentrated in the vertical sideband. Using this idea, this paper proposes the characterization of the texture features of the palmprint using zero-crossing signatures based on the dyadic discrete wavelet transform (DWT) to effectively identify an individual. A zero-crossing signature of 4 x 256 was generated from the lower four resolution levels of dyadic DWT in the enrolment process and stored in the database to identify the person in recognition mode. Euclidean distance was determined to find the best fit for query palmprints zero-crossing signature from the dataset. The proposed algorithm was tested on the PolyU dataset containing 6000 multi-spectral images. The proposed algorithm achieved 96.27% accuracy with a lower recognition time of 0.76 seconds. ABSTRAK: Pengesan Tapak Tangan boleh dikategorikan berdasarkan ciri-ciri tekstur dan corak pada tekstur yang didominasi pada garis tegak. Oleh itu, pekali tenaga di kawasan transformasi adalah lebih penuh pada jalur-sisi menegak. Berdasarkan idea ini, cadangan kajian ini adalah berdasarkan ciri-ciri tekstur pada tapak tangan dan tanda pengenalan sifar-silang melalui transformasi gelombang kecil diadik yang diskret (DWT) bagi mengecam individu. Pada mod pengecaman, tanda pengenalan sifar-silang 4 x 256 yang terhasil daripada tahap diadik resolusi empat terendah DWT digunakan dalam proses kemasukan dan simpanan di pangkalan data bagi mengenal pasti individu. Jarak Euklidan yang terhasil turut digunakan bagi memperoleh padanan tapak tangan paling sesuai melalui tanda pengenalan sifar-silang dari set data.  Algoritma yang dicadangkan ini diuji pada set data PolyU yang mengandungi 6000 imej pelbagai-spektrum. Algoritma yang dicadangkan ini berjaya mencapai ketepatan sebanyak 96.27% dengan durasi pengecaman berkurang sebanyak 0.76 saat.

Weak Gabor bi-frames on periodic subsets of the real line

2015 ◽  
Vol 13 (06) ◽  
pp. 1550046 ◽  
Author(s):  
Yun-Zhang Li ◽  
Hui-Fang Jia
Keyword(s):  
Time Domain ◽  
Real Line ◽  
Positive Measure ◽  
Closed Subspace ◽  
Gabor Frames ◽  
Transform Domain ◽  
Zak Transform ◽  
The Real ◽  
Time Domain Characterization

In this paper, we introduce the concept of weak Gabor bi-frame (WGBF) in a general closed subspace [Formula: see text] of [Formula: see text]. It is a generalization of Gabor bi-frame, and is new even if [Formula: see text]. A WGBF for [Formula: see text] contains all information of [Formula: see text] to some extent. Let [Formula: see text], [Formula: see text], and [Formula: see text] be an [Formula: see text]-periodic subset of [Formula: see text] with positive measure. This paper is devoted to characterizing WGBFs for [Formula: see text] of the form [Formula: see text] It is well-known that, if [Formula: see text], the projections of Gabor frames for [Formula: see text] onto [Formula: see text] cannot cover all Gabor frames for [Formula: see text]. This paper presents a Zak transform-domain and a time-domain characterization of WGBFs for [Formula: see text]. These characterizations are new even if [Formula: see text]. Some examples are also provided to illustrate the generality of our theory.

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