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- W1566606951 abstract "We study nega-cyclic ±1 matrices. We obtain preliminary results which are then used to decrease the search space. We find that there are 2, 4, 9, 23, 63, and 187 ip-equivalence classes for lengths 3, 5, 7, 9, 11, and 13 respectively. The matrices we find are used in a variant given here of the Goethals-Seidel array to form Hadamard matrices, the aim being to later check them for suitability for CDMA schemes. Keywords Hadamard matrix, nega-cyclic, ip-equivalence classes, Goethals-Seidel array, variant Goethals-Seidel array, AMS Subject Classification: Primary 05B20, Secondary 62K05, 62K10 Publication Details This article was originally published as Ang, R, Seberry, J and Wysocki, TA, Inequivalence of Nega-cyclic ±1 Matrices, Journal of Combinatorial Mathematics and Combinatorial Computing 56, 2006, 17-32. This journal article is available at Research Online: http://ro.uow.edu.au/infopapers/354 ! # %$'&)(* ,+.-/ 0 1 24353568797;:, A@CBD68 RQS<CT UVQDT?682C35W XYP?3[Z?^]ME9_ `Da b 68< c5I 6RFHZSI b ZSdfe 2 c568IRKM6J82 I5EgchPi1 6j3[6jQkI^^l K?^lCZ ZD7/ZkF.mhUnQS<CT b ZDdfe 2?c56JI K?8Eg6J<C 6 Qk<CT o a K ^l ZMZS7/ZkFqp 796J c5I E9JQk7r@ b ZSdfe 2?c 68I,Qk<4T UV68796J8ZSdfds2C< E9JQtc EgZD<C3up < =DEg< 6J68I Eg<C= v,<CEgwD68I^3[EgchPxZkFyXzZS797gZD< =SZD< = {RKMX oD|SoDo :L2C3[c5I^Qk79E9Q }x~y8Jt k X6 3hc 2CT?P < 68= Qt P? 79E9 ` d Qtc I5E 6j3 a X6ZDN?c QSEg< e I 6879E9d E9<CQSI5P!I568 3[2C7Gc^3y l E9^l QkI 6 c l 68< 2C356JTsc5Z T?6J8I56jQS356 c5lC6u356JQSI ^l 3[eCQD 6 a Xz6 C<4T c5lCQkc c5lC68I 6LQkI 6 o @DC@DC@ oS @D @ Qk<CT `JM Ege r6jD2CEgwtQk7968<4 6, 7QS3 356J3.FHZSI 7g6J< =kc lC3 @ | @ @k @ `D` @SQS<CT `j I 6J35e46j#c EgwD6879P a Uul 6udfQkc5I E986J3. 6 C<4T QkI 6 2C356JT Eg<xQ wtQSI5EQk< c =SE9wS6J< lC68I 6 ZkFc5l 6RRZ 68c5lCQS793[hKM68ET?6874QkI I QAP c Z FHZSI d QST QSdfQSI Tzd Qtc I5E 6j38@c5l 6xQSEgd)NO68E9< = c5Z7Qtc 68Is^l 6j^]c5lC68d FHZSI,352 Egc QkNCEg79EGchPiFHZSI b R :3 ^l 68df6J3 a xt R ?i8¢;£ ¤?¥¢ ¦§/i8¤?£ k£t © ¤?¢¤?a«¤Mi8¢xa«¤M¬#iJ®. ¥/t° ¤ ±[2A2t3HH2M M ¦/±hkμO¶; ·M¤?3 k¥;2A 2t3 ¤?£ £#k£t .1f 4t¬ §;¤?3 £^± oOkH¢/k3q¤Mi8i8¤k? ;·M¤Mi8H¤?¥4¬ 1 Ot¬ §;¤?3H£#± oOkH¢/k3q¤Mi iJ¤k »f1⁄4 oxo¶/1⁄23⁄4#k2A¬? 3H¤?£8£ A2t¤M¬ ¥ yALi8Ha«¤Mi8  AMAAEAM CoOk2A ¥;¢;¤Mi C?AMx AO C?AM«Et E E;E I.IqIiI«Ð N IyO I E » ¥zO!O O O?OO?×^OOO«O?UU×JU UÞÝs ?aq ?i8¢;tiLaâH£ ¤i£ μO¶;¤Mi a^EMakaxESae,aO¤M¬#i8®«§;¤k·H¥/° ¥;¥/tix¦;i8 O¢;¶2A¬x ?a¢;H£#¬ ¥;2A¬xi Ds£ictti8 /eâ©sk¥2AzÝeÝeeiiia iAðeÞnYo¥/ ?¬# ¬ §¤M¬aoioEMa8A ?i aoooÂeaUa ¢Þ÷4aeJe o Ur×#utuuO?uUROO UU×JUuJýAþi ?au ?i8¢/tiAEay¤Mi x¦y 3 ¥/ a« ¤?3H£ H¥o¬ §/x£ §;Ha ¬AEa«¤M¬#i8 ® i  E     E  eee eee    E E   Â" @default.
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- W1566606951 title "Inequivalence of Nega-cyclic +-1 Matrices" @default.
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