Field element(polynomial notation) 4-tuple representation
0 0000(0 )
1 0001(1 )
a^1 0010(2 )
a^2 0100(4 )
a^3 1000(8 )
a^4 = 1+a 0011(3 )
a^5 = a+a^2 0110(6 )
a^6 = a^2+a^3 1100(12)
a^7 = 1+a+a^3 1011(11)
a^8 = 1+a^3 0101(5 )
a^9 = a+a^3 1010(10)
a^10 = 1+a+a^3 0111(7 )
a^11 = a+a^3+a^3 1110(14)
a^12 = 1+a+a^2+a^3 1111(15)
a^13 = 1+a^2+a^3 1101(13)
a^14 = 1+a^3 1001(9 )
GF(8) 元素如下 GF(2^8 ) 1+x^2+x^3+x^4+x^8
Field element(polynomial notation) 4-tuple representation
0 0000_0000(0 )
1 0000_0001(1 )
a^1 0000_0010(2 )
a^2 0000_0100(4 )
a^3 0000_1000(8 )
a^4 0001_0000(16 )
a^5 0010_0000(32 )
a^6 0100_0000(64 )
a^7 1000_0000(128)
a^8 0001_1101(29 )
a^9 0011_1010(58 )
a^10 0111_0100(116)
a^11 1110_1000(232)
a^12 1100_1101(205)
a^13 1000_0111(135)
a^14 0001_0011(19 )
a^15 0010_0110(38 )
a^16 0100_1100(76 )
a^17 1001_1000(152)
a^18 0010_1101(45 )
a^19 0101_1010(90 )
a^20 1011_0100(180)
a^21 0111_0101(117)
a^22 1110_1010(234)
a^23 1100_1001(201)
a^24 1000_1111(143)
a^25 0000_0011(3 )
a^26 0000_0110(6 )
a^27 0000_1100(12 )
a^28 0001_1000(24 )
a^29 0011_0000(48 )
a^30 0110_0000(96 )
a^31 1100_0000(192)
a^32 1001_1101(157)
a^33 0010_0111(39 )
a^34 0100_1110(78 )
a^35 1001_1100(156)
a^36 0010_0101(37 )
a^37 0100_1010(74 )
a^38 1001_0100(148)
a^39 0011_0101(53 )
a^40 0110_1010(106)
a^41 1101_0100(212)
a^42 1011_0101(181)
a^43 0111_0111(119)
a^44 1110_1110(238)
a^45 1100_0001(193)
a^46 1001_1111(159)
a^47 0010_0011(35 )
a^48 0100_0110(70 )
a^49 1000_1100(140)
a^50 0000_0101(5 )
a^51 0000_1010(10 )
a^52 0001_0100(20 )
a^53 0010_1000(40 )
a^54 0101_0000(80 )
a^55 1010_0000(160)
a^56 0101_1101(93 )
a^57 1011_1010(186)
a^58 0110_1001(105)
a^59 1101_0010(210)
a^60 1011_1001(185)
a^61 0110_1111(111)
a^62 1101_1110(222)
a^63 1010_0001(161)
a^64 0101_1111(95 )
a^65 1011_1110(190)
a^66 0110_0001(97 )
a^67 1100_0010(194)
a^68 1001_1001(153)
a^69 0010_1111(47 )
a^70 0101_1110(94 )
a^71 1011_1100(188)
a^72 0110_0101(101)
a^73 1100_1010(202)
a^74 1000_1001(137)
a^75 0000_1111(15 )
a^76 0001_1110(30 )
a^77 0011_1100(60 )
a^78 0111_1000(120)
a^79 1111_0000(240)
a^80 1111_1101(253)
a^81 1110_0111(231)
a^82 1101_0011(211)
a^83 1011_1011(187)
a^84 0110_1011(107)
a^85 1101_0110(214)
a^86 1011_0001(177)
a^87 0111_1111(127)
a^88 1111_1110(254)
a^89 1110_0001(225)
a^90 1101_1111(223)
a^91 1010_0011(163)
a^92 0101_1011(91 )
a^93 1011_0110(182)
a^94 0111_0001(113)
a^95 1110_0010(226)
a^96 1101_1001(217)
a^97 1010_1111(175)
a^98 0100_0011(67 )
a^99 1000_0110(134)
a^100 0001_0001(17 )
a^101 0010_0010(34 )
a^102 0100_0100(68 )
a^103 1000_1000(136)
a^104 0000_1101(13 )
a^105 0001_1010(26 )
a^106 0011_0100(52 )
a^107 0110_1000(104)
a^108 1101_0000(208)
a^109 1011_1101(189)
a^110 0110_0111(103)
a^111 1100_1110(206)
a^112 1000_0001(129)
a^113 0001_1111(31 )
a^114 0011_1110(62 )
a^115 0111_1100(124)
a^116 1111_1000(248)
a^117 1110_1101(237)
a^118 1100_0111(199)
a^119 1001_0011(147)
a^120 0011_1011(59 )
a^121 0111_0110(118)
a^122 1110_1100(236)
a^123 1100_0101(197)
a^124 1001_0111(151)
a^125 0011_0011(51 )
a^126 0110_0110(102)
a^127 1100_1100(204)
a^128 1000_0101(133)
a^129 0001_0111(23 )
a^130 0010_1110(46 )
a^131 0101_1100(92 )
a^132 1011_1000(184)
a^133 0110_1101(109)
a^134 1101_1010(218)
a^135 1010_1001(169)
a^136 0100_1111(79 )
a^137 1001_1110(158)
a^138 0010_0001(33 )
a^139 0100_0010(66 )
a^140 1000_0100(132)
a^141 0001_0101(21 )
a^142 0010_1010(42 )
a^143 0101_0100(84 )
a^144 1010_1000(168)
a^145 0100_1101(77 )
a^146 1001_1010(154)
a^147 0010_1001(41 )
a^148 0101_0010(82 )
a^149 1010_0100(164)
a^150 0101_0101(85 )
a^151 1010_1010(170)
a^152 0100_1001(73 )
a^153 1001_0010(146)
a^154 0011_1001(57 )
a^155 0111_0010(114)
a^156 1110_0100(228)
a^157 1101_0101(213)
a^158 1011_0111(183)
a^159 0111_0011(115)
a^160 1110_0110(230)
a^161 1101_0001(209)
a^162 1011_1111(191)
a^163 0110_0011(99 )
a^164 1100_0110(198)
a^165 1001_0001(145)
a^166 0011_1111(63 )
a^167 0111_1110(126)
a^168 1111_1100(252)
a^169 1110_0101(229)
a^170 1101_0111(215)
a^171 1011_0011(179)
a^172 0111_1011(123)
a^173 1111_0110(246)
a^174 1111_0001(241)
a^175 1111_1111(255)
a^176 1110_0011(227)
a^177 1101_1011(219)
a^178 1010_1011(171)
a^179 0100_1011(75 )
a^180 1001_0110(150)
a^181 0011_0001(49 )
a^182 0110_0010(98 )
a^183 1100_0100(196)
a^184 1001_0101(149)
a^185 0011_0111(55 )
a^186 0110_1110(110)
a^187 1101_1100(220)
a^188 1010_0101(165)
a^189 0101_0111(87 )
a^190 1010_1110(174)
a^191 0100_0001(65 )
a^192 1000_0010(130)
a^193 0001_1001(25 )
a^194 0011_0010(50 )
a^195 0110_0100(100)
a^196 1100_1000(200)
a^197 1000_1101(141)
a^198 0000_0111(7 )
a^199 0000_1110(14 )
a^200 0001_1100(28 )
a^201 0011_1000(56 )
a^202 0111_0000(112)
a^203 1110_0000(224)
a^204 1101_1101(221)
a^205 1010_0111(167)
a^206 0101_0011(83 )
a^207 1010_0110(166)
a^208 0101_0001(81 )
a^209 1010_0010(162)
a^210 0101_1001(89 )
a^211 1011_0010(178)
a^212 0111_1001(121)
a^213 1111_0010(242)
a^214 1111_1001(249)
a^215 1110_1111(239)
a^216 1100_0011(195)
a^217 1001_1011(155)
a^218 0010_1011(43 )
a^219 0101_0110(86 )
a^220 1010_1100(172)
a^221 0100_0101(69 )
a^222 1000_1010(138)
a^223 0000_1001(9 )
a^224 0001_0010(18 )
a^225 0010_0100(36 )
a^226 0100_1000(72 )
a^227 1001_0000(144)
a^228 0011_1101(61 )
a^229 0111_1010(122)
a^230 1111_0100(244)
a^231 1111_0101(245)
a^232 1111_0111(247)
a^233 1111_0011(243)
a^234 1111_1011(251)
a^235 1110_1011(235)
a^236 1100_1011(203)
a^237 1000_1011(139)
a^238 0000_1011(11 )
a^239 0001_0110(22 )
a^240 0010_1100(44 )
a^241 0101_1000(88 )
a^242 1011_0000(176)
a^243 0111_1101(125)
a^244 1111_1010(250)
a^245 1110_1001(233)
a^246 1100_1111(207)
a^247 1000_0011(131)
a^248 0001_1011(27 )
a^249 0011_0110(54 )
a^250 0110_1100(108)
a^251 1101_1000(216)
a^252 1010_1101(173)
a^253 0100_0111(71 )
a^254 1000_1110(142)
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