• Title, Summary, Keyword: codes

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CYCLIC AND CONSTACYCLIC SELF-DUAL CODES OVER Rk

  • Karadeniz, Suat;Kelebek, Ismail Gokhan;Yildiz, Bahattin
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.4
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    • pp.1111-1122
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    • 2017
  • In this work, we consider constacyclic and cyclic self-dual codes over the rings $R_k$. We start with theoretical existence results for constacyclic and cyclic self-dual codes of any length over $R_k$ and then construct cyclic self-dual codes over $R_1={\mathbb{F}}_2+u{\mathbb{F}}_2$ of even lengths from lifts of binary cyclic self-dual codes. We classify all free cyclic self-dual codes over $R_1$ of even lengths for which non-trivial such codes exist. In particular we demonstrate that our constructions provide a counter example to a claim made by Batoul et al. in [1] and we explain why their claim fails.

QUADRATIC RESIDUE CODES OVER ℤ16

  • Kim, Sung Jin
    • Korean Journal of Mathematics
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    • v.11 no.1
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    • pp.57-64
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    • 2003
  • We define $Z_16$ quadratic residue codes in term of their idempotent generators and show that these codes also have many good properties which are analogous in many respects to properties of quadratic residue codes over a field.

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Locally Repairable Fractional Repetition Codes (부분접속 복구 가능한 반복분할 부호)

  • Nam, Mi-Young;Kim, Jung-Hyun;Song, Hong-Yeop
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.40 no.9
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    • pp.1741-1753
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    • 2015
  • In this paper, we introduce new locally repairable codes based on a Fractional repetition codes which is one of the MBR codes. We introduce two different constructions for different system parameters and compare these codes in terms of several performance metrics. There is some tradeoffs between the locality and other performance metrics. The newly introduced codes having the good locality should pay the price such as lower capacity or more storage nodes. And the proposed codes are more reliable than other locally repairable codes and have lower repair complexity since they can be repaired without any operations.

BASIC CODES OVER POLYNOMIAL RINGS

  • Park, Young Ho
    • Korean Journal of Mathematics
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    • v.15 no.1
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    • pp.79-85
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    • 2007
  • We study codes over the polynomial ring $\mathbb{F}_q[D]$ and introduce the notion of basic codes which play a fundamental role in the theory.

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A class of multi-level spreading codes with enhanced ZCD property

  • Cha, Jae-sang
    • Proceedings of the IEEK Conference
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    • pp.1705-1708
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    • 2002
  • Spreading codes with ZCD(zero-correlation duration) property have the MAI(multiple access interference) rejection ability in the CDMA systems. A class of multi-level spreading codes, i.e., Zero padded ternary ZCD codes are introduced in this paper. By the selected zero-padding method to the binary ZCD codes, ternary ZCD codes are generated and they have enhanced ZCD property and family size than the binary ZCD codes.

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Runlength Limited Codes based on Convolutional Codes

  • Kim, Jeong-Goo
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.26 no.8A
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    • pp.1437-1440
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    • 2001
  • We present a modification method for runlength limited codes based on convolutional codes. This method is based on cosets of convolutional codes and can be applied to any convolutional code without degradation of error control performance of the codes. The upper bound of maximum zero and/or one runlength are provided. Some convolutional codes which have the shortest maximum runlength for given coding parameters are tabulated.

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DC-free error correcting codes based on convolutional codes (길쌈부호를 이용한 무직류 오류정정부호)

  • 이수인;김정구;주언경
    • Journal of the Korean Institute of Telematics and Electronics A
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    • v.32A no.5
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    • pp.24-30
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    • 1995
  • A new class of DC-error correcting codes based on convolutional codes is proposed with its performance analysis. The proposed codes can be encoded and decoded using the conventional convolutional encoders and decoders with slight modifications. And the codes have null point at DC and capable of correcting errors. The DC-free error correcting codes are especially well suited for applications in high-speed channels.

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SELF-DUAL CODES OVER ℤp2 OF SMALL LENGTHS

  • Choi, Whan-hyuk;Park, Young Ho
    • Korean Journal of Mathematics
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    • v.25 no.3
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    • pp.379-388
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    • 2017
  • Self-dual codes of lengths less than 5 over ${\mathbb{Z}}_p$ are completely classified by the second author [The classification of self-dual modular codes, Finite Fields Appl. 17 (2011), 442-460]. The number of such self-dual codes are also determined. In this article we will extend the results to classify self-dual codes over ${\mathbb{Z}}_{p^2}$ of length less than 5 and give the number of codes in each class. Explicit and complete classifications for small p's are also given.

Construction of A Class of Traceability Codes (트래시빌리티 부호 계열의 구조)

  • Ma, Yizhou;Yan, Yier;Lee, Moon-Ho
    • Proceedings of the KIEE Conference
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    • pp.357-359
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    • 2007
  • In order to protect copyrighted materials, codes may be embedded in the content -to trace the traitors. Traceability (TA) codes, as a kind of such codes, have been extensively studied in the intervening years for use as a piracy deterrent. In this correspondence, we proposed a method to construct a class of traceability codes and gave out some parameters results of such codes.

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Performance Analysis of MAP Algorithm and Concatenated Codes Using Trellis of Block Codes (블록부호의 트렐리스를 이용한 MAP 알고리즘 및 연접부호의 성능분석)

  • 백동철;양경철
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.24 no.6A
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    • pp.905-912
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    • 1999
  • In this paper we explain a trellis representation of block codes and derive their MAP decoding algorithm based on it. We also analyze the performance of block codes and concatenated codes with block codes as components by computer simulations, which were performed by changing the structures and constituent codes of concatenated codes. Computer simulations show that soft decision decoding of block codes get an extra coding gain than their hard decision decoding and that concatenated codes using block codes have good performance in the case of high code rate.

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