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Implementation of Self-Correcting Codes for 100 Gb/s Ethernet
Velecký, Jan ; Kučera, Jan (referee) ; Kekely, Lukáš (advisor)
The thesis deals with the design of entire RS-FEC layer for the 100 Gb/s Ethernet according to IEEE 802.3-2015 standard including Reed-Solomon encoder and decoder. Text clarifies mathematical basis of finite fields, linear block codes, cyclic codes and particularly Reed-Solomon codes used in design. Design of RS-FEC layer transmit side has been adjusted for implementation in COMBO network cards which use Xilinx Virtex-7 FPGA and realized in VHDL. Encoder has been optimized in several steps - as for FPGA resource usage and as for VHDL code synthesis duration. Reduction of resource usage has been achieved by using pipelining thanks to properties of cyclic codes. Synthesis duration then by creating logic of encoder on gate level on its own. Resulting implementation has been tested in simulation and it is optimized enough for usage in FPGA for Ethernet implementation. It is possible to adapt both design and implementation for 400Gb/s Ethernet which does not exist yet at the time of design.
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General Codes with m Marks
Holešovský, Jan ; Hrdina, Jaroslav (referee) ; Skula, Ladislav (advisor)
This bachelor's thesis is concerned with results of error-correcting codes theory, which deals with detection and correction of errors, that arise during communication by means of these codes. The aim of this thesis is the explanation of the theory above in absolute generality, followed by detail view of some significant codes. Using linear algebra over finite fields, we will introduce an error-corecting code like a set with structure, whose characters considerably simplify the detection and correction of errors. The knowledge, that was acquired for general codes, is applied to well-known binary codes at the end of the thesis (ie. Hamming codes and Golay code). With these codes are demonstrated their properties, that sort these codes to the most important binary codes.
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Implementation of Self-Correcting Codes for 100 Gb/s Ethernet
Velecký, Jan ; Kučera, Jan (referee) ; Kekely, Lukáš (advisor)
The thesis deals with the design of entire RS-FEC layer for the 100 Gb/s Ethernet according to IEEE 802.3-2015 standard including Reed-Solomon encoder and decoder. Text clarifies mathematical basis of finite fields, linear block codes, cyclic codes and particularly Reed-Solomon codes used in design. Design of RS-FEC layer transmit side has been adjusted for implementation in COMBO network cards which use Xilinx Virtex-7 FPGA and realized in VHDL. Encoder has been optimized in several steps - as for FPGA resource usage and as for VHDL code synthesis duration. Reduction of resource usage has been achieved by using pipelining thanks to properties of cyclic codes. Synthesis duration then by creating logic of encoder on gate level on its own. Resulting implementation has been tested in simulation and it is optimized enough for usage in FPGA for Ethernet implementation. It is possible to adapt both design and implementation for 400Gb/s Ethernet which does not exist yet at the time of design.
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Quasi-monoidic codes
Snítilá, Jitka ; Žemlička, Jan (advisor) ; Šťovíček, Jan (referee)
This thesis focuses on the problem of the key size in McEliece cryptosystem and its solution using quasi- monoidic codes, especially quasi-monoidic Goppa codes. Required theory of quasi-monoidic Cauchy matrices and Goppa codes is introduced along with algebraic structures necessary for quasi-monoidic codes description. Suitable Abelian groups for this class of codes are specified. This thesis also presents efficient algorithms for constructing quasi-monoidic Cauchy matrices and quasi-monoidic Goppa codes. Reduction of the key size using this class of algebraic codes is presented as well. Powered by TCPDF (www.tcpdf.org)
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General Codes with m Marks
Holešovský, Jan ; Hrdina, Jaroslav (referee) ; Skula, Ladislav (advisor)
This bachelor's thesis is concerned with results of error-correcting codes theory, which deals with detection and correction of errors, that arise during communication by means of these codes. The aim of this thesis is the explanation of the theory above in absolute generality, followed by detail view of some significant codes. Using linear algebra over finite fields, we will introduce an error-corecting code like a set with structure, whose characters considerably simplify the detection and correction of errors. The knowledge, that was acquired for general codes, is applied to well-known binary codes at the end of the thesis (ie. Hamming codes and Golay code). With these codes are demonstrated their properties, that sort these codes to the most important binary codes.
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Galoisova tělesa
Horák, Martin
Horák, M. Galois fields. Brno: Mendel University, 2014. This bachelor thesis deals with creating the application for explaining how Galois fields work. It describes the principal of generating elements of the field and how mathematical operations between these elements work. It also deals with using of these fields for cryptography.
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