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短碼長(zhǎng)四元最優(yōu)局部修復(fù)碼的構(gòu)造

李瑞虎 展秀珍 付強(qiáng) 張茂 鄭尤良

李瑞虎, 展秀珍, 付強(qiáng), 張茂, 鄭尤良. 短碼長(zhǎng)四元最優(yōu)局部修復(fù)碼的構(gòu)造[J]. 電子與信息學(xué)報(bào), 2021, 43(12): 3749-3757. doi: 10.11999/JEIT200740
引用本文: 李瑞虎, 展秀珍, 付強(qiáng), 張茂, 鄭尤良. 短碼長(zhǎng)四元最優(yōu)局部修復(fù)碼的構(gòu)造[J]. 電子與信息學(xué)報(bào), 2021, 43(12): 3749-3757. doi: 10.11999/JEIT200740
Ruihu LI, Xiuzhen ZHAN, Qiang FU, Mao ZHANG, Youliang ZHENG. Constructions of Quaternary Optimal Locally Repairable Code with Short Length[J]. Journal of Electronics & Information Technology, 2021, 43(12): 3749-3757. doi: 10.11999/JEIT200740
Citation: Ruihu LI, Xiuzhen ZHAN, Qiang FU, Mao ZHANG, Youliang ZHENG. Constructions of Quaternary Optimal Locally Repairable Code with Short Length[J]. Journal of Electronics & Information Technology, 2021, 43(12): 3749-3757. doi: 10.11999/JEIT200740

短碼長(zhǎng)四元最優(yōu)局部修復(fù)碼的構(gòu)造

doi: 10.11999/JEIT200740
基金項(xiàng)目: 國(guó)家自然科學(xué)基金(11801564, 11901579),陜西省自然科學(xué)基金(2021JM-216, 2021JQ-335),空軍工程大學(xué)基礎(chǔ)部研究生創(chuàng)新基金
詳細(xì)信息
    作者簡(jiǎn)介:

    李瑞虎:男,1966年生,教授,博士生導(dǎo)師,主要研究方向?yàn)槿赫?、圖論、編碼和密碼學(xué)

    展秀珍:女,1995年生,碩士生,研究方向?yàn)榇髷?shù)據(jù)存儲(chǔ)編碼

    付強(qiáng):男,1989年生,講師,博士,研究方向?yàn)樯溆皫缀巍⒔?jīng)典編碼與量子糾錯(cuò)碼

    張茂:男,1996年生,碩士,研究方向?yàn)榫幋a理論

    鄭尤良:男,1996年生,碩士,研究方向?yàn)榉植际酱鎯?chǔ)編碼和糾刪碼

    通訊作者:

    李瑞虎 liruihu@aliyun.com

  • 中圖分類(lèi)號(hào): TN918.3; O157.4

Constructions of Quaternary Optimal Locally Repairable Code with Short Length

Funds: The National Science Foundation of China (11801564, 11901579), Shaanxi Natural Science Foundation (2021JM-216, 2021JQ-335), The Graduate Scientific Research Foundation of Fundamentals Department of Air Force Engineering University
  • 摘要: 在分布式存儲(chǔ)系統(tǒng)中,當(dāng)節(jié)點(diǎn)發(fā)生故障時(shí)局部修復(fù)碼(LRC)可以通過(guò)訪問(wèn)少量其他節(jié)點(diǎn)來(lái)恢復(fù)數(shù)據(jù),然而LRC的局部度不盡相同,該文構(gòu)造了短碼長(zhǎng)且局部度較小的四元LRC。當(dāng)碼長(zhǎng)不超過(guò)20,最小距離大于2時(shí),若四元距離最優(yōu)線性碼的生成陣維數(shù)不超過(guò)校驗(yàn)陣維數(shù),可利用其生成陣給出LRC,否則利用其校驗(yàn)陣給出LRC。對(duì)已構(gòu)造的LRC的生成陣或校驗(yàn)陣,利用刪除、并置等方法得到新矩陣,從而構(gòu)造出190個(gè)碼長(zhǎng)$n \le 20$,最小距離$d \ge 2$的LRC。除12個(gè)LRC外,其他LRC是局部度最優(yōu)的。
  • 表  1  $d \ge 3$, $n \le 20$時(shí)四元LRC的結(jié)果

    n/k123456789
    33(1)
    44(1)3(2)
    55(1)4(2)3(3)
    66(1)4(1)4(3)
    77(1)5(2)4(2)3(3)
    88(1)6(1)5(2)4(3)3(4)
    99(1)7(2)6(2)5(3)4(4)3(4)
    1010(1)8(1)6(1)6(3)5(4)4(5)3(5)
    1111(1)8(1)7(2)6(3)6(4)5(5)4(6)3(6)
    1212(1)9(1)8(1)7(3)6(3)6(5)4(3)4(6)3(6)
    1313(1)10(1)9(2)8(3)7(3)6(4)5(4)4(4)4(7)
    1414(1)11(1)10(2)9(3)8(3)7(4)6(4)5(5)4(4)
    1515(1)12(1)11(2)10(3)8(3)8(4)7(5)6(5)5(5)
    1616(1)12(1)12(2)11(3)9(3)8(4)8(5)7(6)6(5)
    1717(1)13(1)12(2)12(3)10(3)9(4)8(5)8(6)7(7)
    1818(1)14(1)13(2)12(3)10(2)10(4)9(5)8(5)8(7)
    1919(1)15(1)14(2)12(2)11(3)10(3)9(5)8(5)8(6)
    2020(1)16(1)15(2)13(2)12(3)11(3)10(5)9(4)8(5)
    n/k1011121314151617
    133(7)
    144(8)3(8)
    154(4)4(9)3(9)
    165(6)4(5)4(10)3(10)
    176(6)5(7)4(5)4(11)3(11)
    186(6)6(6)5(8)4(5)3(7)3(12)
    197(6)6(7)6(7)5(9)4(6)3(8)3(13)
    208(7)7(7)6(7)6(7)5(10)4(7)3(9)3(14)
    下載: 導(dǎo)出CSV
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出版歷程
  • 收稿日期:  2020-08-24
  • 修回日期:  2021-04-12
  • 網(wǎng)絡(luò)出版日期:  2021-06-04
  • 刊出日期:  2021-12-21

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