• The Journal of the Korea institute of electronic communication sciences
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• v.13 no.4
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• pp.819-826
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• 2018

The generalized Hamming weight is one of the important parameters of the linear code. It determines the performance of the code when the linear codes are applied to a cryptographic system. In addition, when the block code is decoded by soft decision using the lattice diagram, it becomes a measure for evaluating the state complexity required for the implementation. In particular, a bit-parallel multiplier on finite fields based on trinomials have been studied. Cellular automata(CA) has superior randomness over LFSR due to its ability to update its state simultaneously by local interaction. In this paper, we deal with the efficient synthesis of the pseudo random number generator, which is one of the important factors in the design of effective cryptosystem. We analyze the property of the characteristic polynomial of the simple 90/150 transition rule block, and propose a synthesis algorithm of the reversible 90/150 CA corresponding to the trinomials $x^2^n+x^{2^n-1}+1$($n{\geq}2$) and the 90/150 reversible CA(RCA) corresponding to the maximum weight polynomial with $2^n$ degree by using this rule block.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.18 no.8
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• pp.1128-1135
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• 1993

In this paper, new binary cyclic codes (hereafter, refered to as GMW code) which are generated by using GMW sequence, g(t) = tr((trk(a))r), and its cyclic shifts are introduced. Code length of GMW codes is 2a-1, where k is composite integer, e·J. Dimension of the GMW codes is k(k/j)w-1, where w is a Hamming weight of r. Several properties of GMW codes such as designed distance, minimum distance, and weights of code words are obtained in terms of parameters of GMW sequences. And expansion of GMW sequences in terms of m-sequence and its decimation sequences are introduced and characteristic polynomials of GMW sequences are also derived.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.37 no.6A
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• pp.438-449
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• 2012

This paper presents new CRC-p codes for VHF band maritime wireless communication system based on performance analysis of various CRC codes. For this purpose, we firstly describe the method of determination of undetected error probability and minimum Hamming distance according to variation of CRC codeword length. By using the fact that the dual code of cyclic Hamming code and primitive BCH code become maximum length codes, we present an algorithm for computation of undetected error probability and minimum Hamming distance where the concept of simple hardware that is consisted of linear feedback shift register is utilized to compute the weight distribution of CRC codes. We also present construction of transmit data frame of VHF band maritime wireless communication system and specification of major communication parameters. Finally, new optimal CRC-p codes are presented based on the simulation results of undetected error probability and minimum Hamming distance using the various generator polynomials of CRC codes, and their performances are evaluated with simulation results of bit error rate based on the Rician maritime channel model and ${\pi}$/4-DQPSK modulator.