16340

1694 دكتري

دكتري

نظريه جبري كدينگ و رمزنگاري

اصفهان : دانشگاه صنعتي اصفهان

1399

ده، 145ص. :مصور، جدول، نمودار

مرتضي اسماعيلي

محمدحسام تدين

مهرداد تاكي، محمدعلي خسروي فرد، محمود بهبودي

1399/12/06

كتابنامه

رياضي محض

رياضي

1399/12/16

2667925

Coding and Data Storage Locally Repairable Codes Based on Combinatorial Designs Ehsan Yavari ehsan yavari@math iut ac ir eyavari1988@gmail com December 10 2020 Doctor of Philosophy Thesis Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Morteza Esmaeili mesmaeili@cc iut ac ir mesmaeil@engr uvic ca Advisor Dr Mohammad Hesam Tadayon mhtadayon@gmail com Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Iran Telecommunication Research Center ITRC Tehran 14399 55471 Iran Abstract An enormous quantity of data is generated and stored in distributed storage sys tems DSS every day Locally repairable codes LRCs are important because of theirapplications in DSS Let C denote an rn k ds linear code having block length n di mension k and minimum distance d The i th coordinate 1 i n of C is said tohave locality r if the value at this coordinate can be repaired by accessing at most r r k other coordinates and performing a linear computation The code C is calledan LRC with locality r if the i th coordinate of C can be repaired by accessing riother coordinates for each 1 i n In DSS multiple failed nodes may occur at atime and DSS must be able to repair as many failed nodes as possible There aretwo strategies to repairing multiple failed nodes parallel approach and sequentialapproach In the parallel mode the t failed nodes can be repaired simultaneously whereas in the sequential mode the u failed nodes are repaired one by one and anypreviously repaired node can be used to repair the remaining failed nodes In this thesis a new approach is proposed for repairing multiple failed nodes Thejoint sequential parallel approach is proposed with the aim of reducing the repair timein sequential mode Also we study the pn k r t uq ELRCs Exact locally repairablecodes which are rn ks linear codes with the property that any set of failed nodes ofsize at most t can be simultaneously repaired in parallel mode and each element of aset E of failed nodes of size at most u can be sequentially repaired by r r k othercoordinates We present a method by which with a given parity check matrix of an

مرتضي اسماعيلي

محمدحسام تدين

مهرداد تاكي، محمدعلي خسروي فرد، محمود بهبودي