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<meta content="Journal HomePage: http://www.springerlink.com/link.asp?id=103374.   Our joint work on this project started during a visit ofthe first and fourth authors to the University of Tasmania on sabbatical from Louisiana State University in 2003. The second and third authors have been supported by Australian 
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<meta content="[1] Alfaro, R. and A. V. Kelarev, Recent results on ring constructions for error-correcting codes, &quot;Structures and Their Representations&quot;, XV Coloquio Latinoamericano de Algebra (Cocoyoc, Morelos, Mexico, July 20-“26, 2003), Contemporary Math. 376 (2005), 1-12. 

[2] Alfaro, R. and A. V. Kelarev, On cyclic codes in incidence rings, Studia Sci. Math. Hungarica 43(1) (2006), 69-77. 

[3] Araujo, I. M., A. V. Kelarev and A. Solomon, An 
algorithm for commutative semigroup algebras which are principal ideal rings with identity, Comm. Algebra. 32(4) (2004), 1237-“1254. 

[4] Atiyah, M. and I. McDonald, &quot;œIntroduction to Commutative Algebra&quot;, Addison-Wesley, 1969. 

[5] Berman, S. D., On the theory of group codes, Cibernetics 3 (1967), 25-“31. 

[6] Campbell, C. M., E. F. Robertson, N. Ru.skuc and R. M. Thomas, Reidemeister-Schreier type rewriting for semigroups, Semigroup Forum 51 (1995), 47-“62. 

[7] Cazaran, J. and A. V. Kelarev, Generators and weights of polynomial codes, Arch. Math. (Basel) 69 (1997), 479-486. 

[8] Charpin, P., The Reed-Solomon code as ideals of a modular algebra, C. R. Acad. Sci. Paris Ser. I Math. 294 (1982), 597-600. 

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[12] Cormen, T. H., C. E. Leiserson, R. L. Rivest and C. Stein, &quot;œIntroduction to Algorithms&quot;, MIT Press, Cambridge, 2001. 

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[14] Grillet, P.-A., &quot;œSemigroups. An Introduction to the Structure Theory&quot;, Dekker, New York, 1995. 

[15] Grillet, P.-A., Computing finite commutative semigroups, Semigroup Forum 53 (1996)(2), 140-154. 

[16] Hall, T.E., The radical of the algebra of any finite semigroup over any field, J. Austral. Math. Soc. Ser. A 11 (1970), 350-352. 

[17] Hall, T. E., Biprefix codes, inverse semigroups and syntactic monoids of injective automata, Theoretical Computer Science 32(1-2) (1984), 201-213. 

[18] Howie, J. M., &quot;œFundamentals ofSemigroup Theory&quot;, Clarendon Press, Oxford, 1995. 

[19] Kelarev, A. V., Radicals of semigroup rings of commutative semigroups, Semigroup Forum 48 (1994), 1-17. 

[20] Kelarev, A. V., &quot;Ring Constructions and Applications&quot;, World Scientific, London, 2002. 

[21] Kelarev, A. V., &quot;Graph Algebras and Automata&quot;, Marcel Dekker, New York, 2003. 

[22] Kelarev, A. V., Minimum distances and information rates for matrix extensions of BCH codes, The 3rd Workshop on the Internet, Telecommunications and Signal Processing, WITSP 2004, (Adelaide, 20-22 December 2004), 1-6. 

[23] Kelarev, A. V., A Polynomial Algorithm for Codes Based on Directed Graphs, In Proc. Twelfth Computing: The Australasian Theory Symposium (CATS2006), Hobart, Australia. CRPIT, 51 (2006), J. Gudmundsson and B. Jay, Eds., ACS, 87-92. 

[24] Kelarev, A. V. and O. V. Sokratova, Information rates and weights of codes in structural matrix rings, Lecture Notes in Computer Science 2227 (2001), 151-“158. 

[25] Kelarev, A. V. and P. Sole, Error-correcting codes as ideals in group rings, &quot;Abelian Rings, Groups and Modules&quot;, AGRAM 2000, (September 2000, Perth, Australia), Contemporary Mathematics 273 (2001), 11-18. 

[26] Landrock, P. and O. Manz, Classical codes as ideals in group algebras, Des. Codes and Crypt. 2 (1992), 273-285. 

[27] Lidl, R. and H. Niederreiter, &quot;Introductions to Finite Fields and Their Applications&quot;, Cambridge University Press, Cambridge, 1994. 

[28] Lidl, R. and H. Niederreiter, &quot;œFinite Fields&quot;, Cambridge University Press, Cambridge, 1997. 

[29] Lidl, R. and G. Pilz, &quot;Applied Abstract Algebra&quot;, Springer-Verlag, Berlin, 1998. 

[30] Lidl, R. and J. Wiesenbauer, &quot;Ring Theory and Applications&quot;, Wiesbaden, 1980, in German. 

[31] Okninski, J., &quot;œSemigroup Algebras&quot;, Marcel Dekker, New York, 1991. 

[32] Pless, V. S., W. C. Huffman and R. A. Brualdi, &quot;œHandbook of Coding Theory&quot;, Elsevier, New York, 1998. 

[33] Ponizovski.i, J. S., Semigroup rings, Semigroup Forum 36 (1987), 1-“46. 

[34] Rajan, B. S. and M. U. Siddiqi, Transform domain characterization of abelian codes, IEEE Trans. Inform. Theory 38 (1992), 1817-“1821. 

[35] Renteria, C. and H. Tapia Recillas, Reed-Muller codes: an ideal theory approach, Comm. Algebra 25 (1997), 401-413. 

[36] Rosales, J. C. and P. A. Garcia-Sanchez, &quot;œFinitely Generated Commutative Monoids&quot;, Nova Science Publ., New York, 1999. 

[37] Ru.skuc, N., Presentations for subgroups of monoids, J. Algebra 220(1) (1999), 365-“380. 

[38] Sims, C. C., &quot;Computation with Finitely Presented Groups&quot;, University Press, Cambridge, 1994. 

[39] Sabin, R. E., On minimum distance bounds for abelian codes, Appl. Algebra Engrg. Comm. Comput. 3 (1992), 183-“197. 

[40] Shevrin, L. N. and A. Ja. Ovsyannikov, &quot;œSemigroups and their Subsemigroup Lattices&quot;, Kluwer, Dordrecht, 1996. 

[41] Stallings, W., &quot;Wireless Communications and Networking&quot;, Prentice Hall, 2002. 

[42] Teply, M. L., E. G. Turman and A. Quesada, On semisimple semigroup rings, Proc. Amer. Math. Soc. 79 (1980), 157-“163. 

[43] Vertigan, Dirk, Latroids and their representation by codes over modules, Trans. Amer. Math. Soc. 356(10) (2004), 3841-3868. 
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    <h1 class="ep_tm_pagetitle">An algorithm for computing the minimum distances of extensions of BCH codes embedded in semigroup rings</h1>
    <p style="margin-bottom: 1em" class="not_ep_block"><span class="person_name">Cazaran, Jilyana</span> and <span class="person_name">Kelarev, Andrei</span> and <span class="person_name">Quinn, Stephen</span> and <span class="person_name">Vertigan, Dirk</span> (2006) <xhtml:em>An algorithm for computing the minimum distances of extensions of BCH codes embedded in semigroup rings.</xhtml:em> Semigroup Forum, 73 . pp. 317-329. ISSN 0037-1912</p><p style="margin-bottom: 1em" class="not_ep_block"></p><table style="margin-bottom: 1em" class="not_ep_block"><tr><td valign="top" style="text-align:center"><a href="http://eprints.utas.edu.au/893/1/kelarev2006.pdf"><img alt="[img]" src="http://eprints.utas.edu.au/style/images/fileicons/application_pdf.png" class="ep_doc_icon" border="0" /></a></td><td valign="top"><a href="http://eprints.utas.edu.au/893/1/kelarev2006.pdf"><span class="ep_document_citation">PDF</span></a> - Full text restricted - Requires a PDF viewer<br />341Kb</td></tr></table><p style="margin-bottom: 1em" class="not_ep_block">Official URL: <a href="http://dx.doi.org/10.1007/s00233-006-0647-9">http://dx.doi.org/10.1007/s00233-006-0647-9</a></p><div class="not_ep_block"><h2>Abstract</h2><p style="padding-bottom: 16px; text-align: left; margin: 1em auto 0em auto">An algorithm is given for computing the weights of extensions of BCH codes embedded in semigroup rings as ideals. The algorithm relies on a more general technical result of independent interest. 
</p></div><table style="margin-bottom: 1em" cellpadding="3" class="not_ep_block" border="0"><tr><th valign="top" class="ep_row">Item Type:</th><td valign="top" class="ep_row">Article</td></tr><tr><th valign="top" class="ep_row">Additional Information:</th><td valign="top" class="ep_row">Journal HomePage: http://www.springerlink.com/link.asp?id=103374.   Our joint work on this project started during a visit ofthe first and fourth authors to the University of Tasmania on sabbatical from Louisiana State University in 2003. The second and third authors have been supported by Australian 
Research Council, Discovery grant DP0449469. 
</td></tr><tr><th valign="top" class="ep_row">Subjects:</th><td valign="top" class="ep_row"><a href="http://eprints.utas.edu.au/view/subjects/280110.html">280000 Information, Computing and Communication Sciences &gt; 280100 Information Systems &gt; 280110 Systems Theory</a><br /><a href="http://eprints.utas.edu.au/view/subjects/280103.html">280000 Information, Computing and Communication Sciences &gt; 280100 Information Systems &gt; 280103 Information Storage, Retrieval and Management</a><br /><a href="http://eprints.utas.edu.au/view/subjects/280506.html">280000 Information, Computing and Communication Sciences &gt; 280500 Data Format &gt; 280506 Coding and Information Theory</a></td></tr><tr><th valign="top" class="ep_row">ID Code:</th><td valign="top" class="ep_row">893</td></tr><tr><th valign="top" class="ep_row">Deposited By:</th><td valign="top" class="ep_row"><span class="ep_name_citation"><span class="person_name">Dr Andrei Kelarev</span></span></td></tr><tr><th valign="top" class="ep_row">Deposited On:</th><td valign="top" class="ep_row">02 Apr 2007</td></tr><tr><th valign="top" class="ep_row">Last Modified:</th><td valign="top" class="ep_row">09 Jan 2008 02:30</td></tr><tr><th valign="top" class="ep_row">ePrint Statistics:</th><td valign="top" class="ep_row"><a target="ePrintStats" href="/es/index.php?action=show_detail_eprint;id=893;">View statistics for this ePrint</a></td></tr></table><p align="right">Repository Staff Only: <a href="http://eprints.utas.edu.au/cgi/users/home?screen=EPrint::View&amp;eprintid=893">item control page</a></p>
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