On "A new representation of elements of finite fields GF(2/sup m/) yielding small complexity arithmetic circuits"

For original article see G. Drolet, ibid., vol. 47, no. 9, p. 938-946, (Sept 1998). We characterize the smallest n with GF(2)[X]/(X/sup n/ + 1) containing an isomorphic copy of GF(2/sup m/). This characterization shows that the representation of finite fields described in a previous issue of the IEE...

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Veröffentlicht in:	IEEE transactions on computers 2002-12, Vol.51 (12), p.1460-1461
Hauptverfasser:	Geiselmann, W., Muller-Quade, J., Steinwandt, R.
Format:	Artikel
Sprache:	eng
Schlagworte:	Arithmetic Circuits Complexity Galois fields Hardware Mathematical analysis Optimization Polynomials Representations Reproduction Very large scale integration
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creator	Geiselmann, W. Muller-Quade, J. Steinwandt, R.
description	For original article see G. Drolet, ibid., vol. 47, no. 9, p. 938-946, (Sept 1998). We characterize the smallest n with GF(2)[X]/(X/sup n/ + 1) containing an isomorphic copy of GF(2/sup m/). This characterization shows that the representation of finite fields described in a previous issue of the IEEE Transactions on Computers is not "optimal" as claimed. The representation considered there can often be improved significantly.
doi_str_mv	10.1109/TC.2002.1146713
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Drolet, ibid., vol. 47, no. 9, p. 938-946, (Sept 1998). We characterize the smallest n with GF(2)[X]/(X/sup n/ + 1) containing an isomorphic copy of GF(2/sup m/). This characterization shows that the representation of finite fields described in a previous issue of the IEEE Transactions on Computers is not "optimal" as claimed. 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Drolet, ibid., vol. 47, no. 9, p. 938-946, (Sept 1998). We characterize the smallest n with GF(2)[X]/(X/sup n/ + 1) containing an isomorphic copy of GF(2/sup m/). This characterization shows that the representation of finite fields described in a previous issue of the IEEE Transactions on Computers is not "optimal" as claimed. The representation considered there can often be improved significantly.</description><subject>Arithmetic</subject><subject>Circuits</subject><subject>Complexity</subject><subject>Galois fields</subject><subject>Hardware</subject><subject>Mathematical analysis</subject><subject>Optimization</subject><subject>Polynomials</subject><subject>Representations</subject><subject>Reproduction</subject><subject>Very large scale integration</subject><issn>0018-9340</issn><issn>1557-9956</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2002</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNp9kc1rGzEQxUVpoK6Tcw69CB-a9rCxvna1OhqTuIFALs5ZaLWjVma_ImlJ_d9XxoZCDz3NvJnfGxgeQreU3FNK1Hq_vWeEsCxEJSn_gBa0LGWhVFl9RAtCaF0oLsgn9DnGAyGkYkQt0NvLgFcbPMA7DjAFiDAkk_w44NFh6KDPOp565wefIBfo2oh3j9_YOs4T7tff8fE088NPHHvTddiO_dTBb5-O2ASffvWQvMXWBzv7FFfX6MqZLsLNpS7R6-PDfvujeH7ZPW03z4UVQqQC2soRSxsmnZTOlk1ra960hDal42UjqaGcSTAWGPBW1ZV0NTSqpNbktXB8ie7Od6cwvs0Qk-59tNB1ZoBxjloRqQSnFcvk1_-SrBaCcy4yuPoHPIxzGPIXuq5FKYSidYbWZ8iGMcYATk_B9yYcNSX6lJTeb_UpKX1JKju-nB0eAP7Sl-0fJDCPCg</recordid><startdate>20021201</startdate><enddate>20021201</enddate><creator>Geiselmann, W.</creator><creator>Muller-Quade, J.</creator><creator>Steinwandt, R.</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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Drolet, ibid., vol. 47, no. 9, p. 938-946, (Sept 1998). We characterize the smallest n with GF(2)[X]/(X/sup n/ + 1) containing an isomorphic copy of GF(2/sup m/). This characterization shows that the representation of finite fields described in a previous issue of the IEEE Transactions on Computers is not "optimal" as claimed. The representation considered there can often be improved significantly.</abstract><cop>New York</cop><pub>IEEE</pub><doi>10.1109/TC.2002.1146713</doi><tpages>2</tpages></addata></record>
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subjects	Arithmetic Circuits Complexity Galois fields Hardware Mathematical analysis Optimization Polynomials Representations Reproduction Very large scale integration
title	On "A new representation of elements of finite fields GF(2/sup m/) yielding small complexity arithmetic circuits"
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