• Title, Summary, Keyword: codes

Search Result 4,706, Processing Time 0.054 seconds

CYCLIC CODES OVER THE RING 𝔽p[u, v, w]/〈u2, v2, w2, uv - vu, vw - wv, uw - wu〉

  • Kewat, Pramod Kumar;Kushwaha, Sarika
    • Bulletin of the Korean Mathematical Society
    • /
    • v.55 no.1
    • /
    • pp.115-137
    • /
    • 2018
  • Let $R_{u{^2},v^2,w^2,p}$ be a finite non chain ring ${\mathbb{F}}_p[u,v,w]{\langle}u^2,\;v^2,\;w^2,\;uv-vu,\;vw-wv,\;uw-wu{\rangle}$, where p is a prime number. This ring is a part of family of Frobenius rings. In this paper, we explore the structures of cyclic codes over the ring $R_{u{^2},v^2,w^2,p}$ of arbitrary length. We obtain a unique set of generators for these codes and also characterize free cyclic codes. We show that Gray images of cyclic codes are 8-quasicyclic binary linear codes of length 8n over ${\mathbb{F}}_p$. We also determine the rank and the Hamming distance for these codes. At last, we have given some examples.

NEGACYCLIC CODES OF LENGTH 8ps OVER Fpm + uFpm

  • Klin-eam, Chakkrid;Phuto, Jirayu
    • Bulletin of the Korean Mathematical Society
    • /
    • v.56 no.6
    • /
    • pp.1385-1422
    • /
    • 2019
  • Let p be an odd prime. The algebraic structure of all negacyclic codes of length $8_{p^s}$ over the finite commutative chain ring ${\mathbb{F}}_{p^m}+u{\mathbb{F}}_{p^m}$ where $u^2=0$ is studied in this paper. Moreover, we classify all negacyclic codes of length $8_{p^s}$ over ${\mathbb{F}}_{p^m}+u{\mathbb{F}}_{p^m}$ into 5 cases, i.e., $p^m{\equiv}1$ (mod 16), $p^m{\equiv}3$, 11 (mod 16), $p^m{\equiv}5$, 13 (mod 16), $p^m{\equiv}7$, 15 (mod 16) and $p^m{\equiv}9$ (mod 16). From that, the structures of dual and some self-dual negacyclic codes and number of codewords of negacyclic codes are obtained.

Multi-dimensional DC-free trellis codes based on tow-dimensional constellation (2차원 성상도를 이용한 다차원 무직류 격자형부호)

  • 정창기;황성준;주언경
    • Journal of the Korean Institute of Telematics and Electronics S
    • /
    • v.35S no.3
    • /
    • pp.47-53
    • /
    • 1998
  • Multi-dimensional DC-free trellis codes based on two-dimensional constellation which can be omplemented more easily than conventional codes are proposed and their performances are analyzed in this paper. 2N-dimensional constellation of the proposed codes is constructed by concatenating N 2-dimensional constellation. Thus, for the proposed codes, information bits can be assigned easily to each signal point of the 2-dimensional consteellation and DC-free characteristic can be simply obtained by the symmetric structure of the constellation. In addition, since Viterbi decoder can calculate multi-dimensional Euchlidean distance between signals by simple sum of each 2-dimensional Euclidean distanc, decoding complexity can be reduced. The performance analysis shows that the proposed codes have almost same spectral characteristic and error performance as compared with conventional codes. However, the complexity is shown to be reduced further due to the construction method of contellation and the simple decoding algorithm of the proposed codes.

  • PDF

Split LDPC Codes for Hybrid ARQ

  • Joo, Hyeong-Gun;Hong, Song-Nam;Shin, Dong-Joon
    • The Journal of Korean Institute of Communications and Information Sciences
    • /
    • v.32 no.10C
    • /
    • pp.942-949
    • /
    • 2007
  • In this paper, we propose a new rate-control scheme, called splining, to construct low-rate codes from high-rate codes by splitting rows of the parity-check matrices of LDPC codes, which can construct rate-compatible LDPC codes having good initial transmission performance. Good low-rate codes can be constructed by making the number of distinct check node degrees as small as possible after splitting. The proposed scheme achieves good cycle property, low decoding complexity, and fast convergence speed, especially compared to the puncturing. Especially, rate-compatible repeat accumulate-type LDPC (RA-Type LDPC) code is constructed using splitting, which covers the code rates from 1/3 to 4/5. Through simulation it is shown that this code outperforms other rate-compatible RA-Type LDPC codes for all rates and can be decoded conveniently and efficiently.

Low BER Channel Coding For WiBro Modem Design (WiBro 모뎀 설계를 위한 Low BER 채널 코딩)

  • Lee, Min-Young;Kim, In-Soo;Min, Hyoung-Bok
    • Proceedings of the KIEE Conference
    • /
    • /
    • pp.2271-2272
    • /
    • 2008
  • Recently, LDPC codes received a lot of attention in 4G. LDPC codes perform good error correction at high SNR. But LDPC codes are complex design and not good at low SNR. At low SNR, convolution codes and turbo codes show more good performance than LDPC codes. The main subject presented in this study is that parallel encoding and decoding according to SNR. The system chooses convolution codes at low SNR and chooses LDPC codes at high SNR.

  • PDF

THE CLASSIFICATION OF SELF-ORTHOGONAL CODES OVER ℤp2 OF LENGTHS ≤ 3

  • Choi, Whan-Hyuk;Kim, Kwang Ho;Park, Sook Young
    • Korean Journal of Mathematics
    • /
    • v.22 no.4
    • /
    • pp.725-742
    • /
    • 2014
  • In this paper, we find all inequivalent classes of self-orthogonal codes over $Z_{p^2}$ of lengths $l{\leq}3$ for all primes p, using similar method as in [3]. We find that the classification of self-orthogonal codes over $Z_{p^2}$ includes the classification of all codes over $Z_p$. Consequently, we classify all the codes over $Z_p$ and self-orthogonal codes over $Z_{p^2}$ of lengths $l{\leq}3$ according to the automorphism group of each code.

ON QUANTUM CODES FROM CYCLIC CODES OVER A CLASS OF NONCHAIN RINGS

  • Sari, Mustafa;Siap, Irfan
    • Bulletin of the Korean Mathematical Society
    • /
    • v.53 no.6
    • /
    • pp.1617-1628
    • /
    • 2016
  • In this paper, we extend the results given in [3] to a nonchain ring $R_p={\mathbb{F}}_p+v{\mathbb{F}}_p+{\cdots}+v^{p-1}{\mathbb{F}}_p$, where $v^p=v$ and p is a prime. We determine the structure of the cyclic codes of arbitrary length over the ring $R_p$ and study the structure of their duals. We classify cyclic codes containing their duals over $R_p$ by giving necessary and sufficient conditions. Further, by taking advantage of the Gray map ${\pi}$ defined in [4], we give the parameters of the quantum codes of length pn over ${\mathbb{F}}_p$ which are obtained from cyclic codes over $R_p$. Finally, we illustrate the results by giving some examples.

LINEAR AND NON-LINEAR LOOP-TRANSVERSAL CODES IN ERROR-CORRECTION AND GRAPH DOMINATION

  • Dagli, Mehmet;Im, Bokhee;Smith, Jonathan D.H.
    • Bulletin of the Korean Mathematical Society
    • /
    • v.57 no.2
    • /
    • pp.295-309
    • /
    • 2020
  • Loop transversal codes take an alternative approach to the theory of error-correcting codes, placing emphasis on the set of errors that are to be corrected. Hitherto, the loop transversal code method has been restricted to linear codes. The goal of the current paper is to extend the conceptual framework of loop transversal codes to admit nonlinear codes. We present a natural example of this nonlinearity among perfect single-error correcting codes that exhibit efficient domination in a circulant graph, and contrast it with linear codes in a similar context.

A Study on the Legislation Types and Prescriptions of American Earth Building Codes (미국 흙건축 법규의 법제화 유형 및 규제내용 분석)

  • Kim, Jeong-Gyu
    • KIEAE Journal
    • /
    • v.8 no.3
    • /
    • pp.19-26
    • /
    • 2008
  • The purpose of this study is to analyze the legislation types and prescriptions of American earth building codes. The process of this study is as follows: (1) To understand the legislation background of American earth building codes, this study investigated the history and present state of earth building techniques which is used in USA. (2) To understand the legislation method and procedure of American earth building codes, this study investigated the legislation system of American building codes and the process of model building codes development and adoption. (3) To provide basic data for the legislation of Korean earth building codes or guidelines, this study analyzed American earth building codes about adobe, compressed earth block and rammed earth. The result of this study is as follows: (1) To meet need of a single coordinated set of national model building codes in the United States, the nation's three model code groups decided to form the International Code Council and the first edition of the International Building Code was published in 1997. In the International Building Code there are prescriptions on adobe construction. (2) There are three legislation types of earth building codes in USA. First is to use prescriptions of International Building Code on adobe construction. Second is that State governments establish and issue a separate document under its own title. The last is that local jurisdictions adopt International Building Code with amendments or additional rules. (3) On the base of analysis of American earth building codes, this study proposed the legislation process and direction of Korean earth building codes and guidelines.