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On cyclotomic cosets and code constructions
Linear Algebra and its Applications, 2016 New properties of $q$-ary cyclotomic cosets modulo $n = q^{m} - 1$, where $q \geq 3$ is a prime power, are investigated in this paper. Based on these properties, the dimension as well as bounds for the designed distance of some families of classical cyclic codes can be computed.
Giuliano Gadioli La Guardia +1 more
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Pelikán's conjecture and cyclotomic cosets
Journal of Combinatorial Theory, Series A, 1977 AbstractThe following conjecture was recently made by J. Pelikán. Let a0 ,…, an be an (n + 1)-tuple of 0's and 1's; let Ak = ϵi=0n−kaiai+k for k = 0,…, n. Then if n ⩾ 4 some Ak is even.This paper shows that Pelikán's conjecture is false for infinitely many values of n. On the other hand it is also shown that the conjecture is true for most values of n,
F. Jessie MacWilliams, Andrew M. Odlyzko
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Some New Quantum BCH Codes over Finite Fields
Entropy, 2021 Quantum error correcting codes (QECCs) play an important role in preventing quantum information decoherence. Good quantum stabilizer codes were constructed by classical error correcting codes.
Lijuan Xing, Zhuo Li
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A General Construction of Integer Codes Correcting Specific Errors in Binary Communication Channels
Mathematics, 2023 Integer codes have been successfully applied to various areas of communication and computer technology. They demonstrate good performance in correcting specific kinds of errors.
Hristo Kostadinov, Nikolai Manev
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Asymmetric Entanglement-Assisted Quantum MDS Codes Constructed from Constacyclic Codes
Entropy, 2023 Due to the asymmetry of quantum errors, phase-shift errors are more likely to occur than qubit-flip errors. Consequently, there is a need to develop asymmetric quantum error-correcting (QEC) codes that can safeguard quantum information transmitted ...
Jianzhang Chen +7 more
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Integer Codes Correcting Asymmetric Errors in Nand Flash Memory
Mathematics, 2021 Memory devices based on floating-gate transistor have recently become dominant technology for non-volatile storage devices like USB flash drives, memory cards, solid-state disks, etc.
Hristo Kostadinov, Nikolai Manev
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Construction of Standard Solid Sudoku Cubes and 3D Sudoku Puzzles
IEEE Access, 2022 In this paper, standard solid Sudoku cubes (SSSCs), a three-dimensional (3D) extension of Sudoku tables, are introduced, and a method to construct these cubes is presented. This is the first class of standard solid Sudoku cubes. An SSSC of order $m$ is
Mehrab Najafian +2 more
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Constacyclic Codes over Finite Chain Rings of Characteristic p
Axioms, 2021 Let R be a finite commutative chain ring of characteristic p with invariants p,r, and k. In this paper, we study λ-constacyclic codes of an arbitrary length N over R, where λ is a unit of R.
Sami Alabiad, Yousef Alkhamees
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Construction of Some New Quantum BCH Codes
IEEE Access, 2018 Classical Bose-Chaudhuri-Hocquenghem (BCH) codes over finite fields have been studied extensively. One can construct quantum stabilizer codes with good parameters using classical BCH codes. In this paper, our goal is to find such classical BCH codes.
Ming Zhang +3 more
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D-Optimal Designs: A Mathematical Programming Approach Using Cyclotomic Cosets [PDF]
Informatica, 2011 In this paper, a novel approach involving the concepts from mathematical programming and number theory is proposed to find the D-optimal designs. In specific, we will propose a mathematical formulation for the D-optimal design. In addition to that, we will present the use of cyclotomic cosets in the mathematical formulation, in order to reduce the ...
Mujahid N. Syed +2 more
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