پديد آورنده :
سبحاني، رضا
عنوان :
ساختار و كاربرد كدهاي دوري و λ- دوري روي برخي از حلقه هاي زنجيري
گرايش تحصيلي :
رياضي كاربردي﴿نظريه كد گذاري﴾
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان،دانشكده علوم رياضي
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
مرتضي اسماعيلي
استاد مشاور :
محمدعلي خسروي فرد
تاريخ نمايه سازي :
4/5/89
استاد داور :
فرشاد لاهوتي،شكرالله سالاريان،محمود بهبودي
كد ايرانداك :
ID307 دكتري
چكيده فارسي :
به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي
چكيده انگليسي :
On the structure and application of cyclic and cyclic codes over some nite chain rings Reza Sobhani sbnreza@math iut ac ir February 20 2010 Doctor of Philosophy Thesis Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Morteza Esmaeili emorteza@cc iut ac ir Advisor Dr Mohammad Ali Khosravifard khosravi@cc iut ac ir Department Graduate Program Coordinator Dr Azam Etemad ae110mat@cc iut ac ir Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Department of Electrical and Computer Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Abstract The discovery of the fact that many known nonlinear codes are the Gray images of certain linear codes over Z4 motivated the study of linear codes over rings in general Among linear codes the structure of linear cyclic codes and generally cyclic codes and among nite rings the rings Zpe and generally nite chain rings have been more studied In this thesis we study the structure of cyclic codes of arbitrary length N over a nite chain ring In the case where R Fpm uFpm or R GR p2 m we classify all linear cyclic codes of arbitrary length N over R and determine their duals As a corollary we list all linear cyclic self dual codes of even length less than or equal m 1 to 16 over the rings F2 uF2 and Z4 Finally by introducing a map from R to Fpm p s called the Gray map we investigate a relationship between 1 cyclic codes of length N over R and quasi cyclic codes of length pms N and index pms 1 over Fpm By considering the ring Fpm u us 1 we introduce an application of the results in the decoding of binary linear repeated root cyclic codes of length 2n n odd Key Words Cyclic codes Chain rings Gray map 1 Introduction The discovery of good nonlinear codes from linear codes over Z4 via the Gray map motivated studying of cyclic codes over rings in general 6 It has been shown in 6 that the polynomial X 3 X 1 generating the binary Hamming code of length 7 over F2 lifts to the polynomial X 3 2X 2 X 3 that generates a cyclic code over the ring Z4 Extending this code over Z4 by adding an overall parity check symbol 1
استاد راهنما :
مرتضي اسماعيلي
استاد مشاور :
محمدعلي خسروي فرد
استاد داور :
فرشاد لاهوتي،شكرالله سالاريان،محمود بهبودي
