mathbb \mathbb [u] –Cyclic and Constacyclic Codes
Following the very recent studies on ℤ 2 ℤ 4 -additive codes, ℤ 2 ℤ 2 [u]-linear codes have been introduced by Aydogdu et al. In this paper, we introduce and study the algebraic structure of cyclic, constacyclic codes and their duals over the R-module Z 2 α R β where R = ℤ 2 +uℤ 2 = {0, 1, u, u + 1}...
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| Veröffentlicht in: | IEEE transactions on information theory 2017-08, Vol.63 (8), p.4883-4893 |
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| creator | Aydogdu, Ismail Abualrub, Taher Siap, Irfan |
| description | Following the very recent studies on ℤ 2 ℤ 4 -additive codes, ℤ 2 ℤ 2 [u]-linear codes have been introduced by Aydogdu et al. In this paper, we introduce and study the algebraic structure of cyclic, constacyclic codes and their duals over the R-module Z 2 α R β where R = ℤ 2 +uℤ 2 = {0, 1, u, u + 1} is the ring with four elements and u 2 = 0. We determine the generating independent sets and the types and sizes of both such codes and their duals. Finally, we present a bound and an optimal family of codes attaining this bound and also give some illustrative examples of binary codes that have good parameters which are obtained from the cyclic codes in Z 2 α R β . |
| doi_str_mv | 10.1109/TIT.2016.2632163 |
| format | Article |
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Finally, we present a bound and an optimal family of codes attaining this bound and also give some illustrative examples of binary codes that have good parameters which are obtained from the cyclic codes in Z 2 α R β .</description><subject>Additives</subject><subject>Binary codes</subject><subject>Binary system</subject><subject>bounds</subject><subject>Codes</subject><subject>constacyclic codes</subject><subject>cyclic codes</subject><subject>duality</subject><subject>Generators</subject><subject>Linear codes</subject><subject>Mathematics</subject><subject>Structural rings</subject><subject>Zinc</subject><subject>Z₂Z₂[<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">u ]-linear cyclic codes</subject><issn>0018-9448</issn><issn>1557-9654</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNo9kE1LAzEQhoMoWKt3wcuC562ZmWSTPcriR6HgpZ5UQpJNsKXt1s320Jv_wX_oL3HLFk8vMzzvDDyMXQOfAPDybj6dT5BDMcGCEAo6YSOQUuVlIcUpG3EOOi-F0OfsIqVlPwoJOGK0tt2nc9n7Md92H9nv90-196uFz-ymzqpmkzrrh0XV1CFdsrNoVylcHXPMXh8f5tVzPnt5mlb3s9wDFZgHUNbZ6CTq6EPtgTsqdFmrGAGF9Z7IxogOtA7aEwaKtuesIxJlFERjdjvc3bbN1y6kziybXbvpXxoEJQhLRdhTfKB826TUhmi27WJt270Bbg5qTK_GHNSYo5q-cjNUFiGEf1wpKbVE-gPjJ1_B</recordid><startdate>201708</startdate><enddate>201708</enddate><creator>Aydogdu, Ismail</creator><creator>Abualrub, Taher</creator><creator>Siap, Irfan</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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| subjects | Additives Binary codes Binary system bounds Codes constacyclic codes cyclic codes duality Generators Linear codes Mathematics Structural rings Zinc Z₂Z₂[<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">u ]-linear cyclic codes |
| title | mathbb \mathbb [u] –Cyclic and Constacyclic Codes |
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