Walsh spectra of all known APN functions over GF(2^8)

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The tables below contain the Walsh spectra for all known instances of APN functions over GF(2^8). All of these 8180 functions have one of the following three Walsh spectra:

  • (same as the Gold functions)
  • (type 1)
  • (type 2)

There are 12 functions with a Walsh spectrum of type 2 (given in the table below), 487 functions with a Walsh spectrum of type 1, and 7681 functions with a Gold-like Walsh spectrum (not listed below due to space limitations). Magma code listing all functions with a Gold-like Walsh spectrum, a Walsh spectrum of type 1 and a Walsh spectrum of type 2 is available.


Functions with Walsh spectrum of type 2
g130 x192 + g160 x160 + g117 x144 + g230 x136 + g228 x132 + g162 x130 + g25 x129 + g79 x96 + g204 x80 + g83 x72 + g159 x68 + g234 x66 + g36 x65 + g67 x48 + g151 x40 + g17 x36 + g81 x34 + g52 x33 + g9 x24 + g116 x20 + g102 x18 + g97 x17 + g74 x12 + g48 x10 + g144 x9 + g58 x6 + g146 x5 + g123x3
g154 x192 + g36 x160 + g83 x144 + g160 x136 + g253 x132 + g215 x130 + g221 x129 + g76 x96 + g137 x80 + g206 x72 + g185 x68 + g165 x66 + g201 x65 + g226 x48 + g25 x40 + g65 x36 + g11 x33 + g170 x24 + g247 x20 + g155 x18 + g x17 + g146 x12 + g204 x10 + g121 x9 + g202 x6 + g246 x5 + g170 x3
g183 x192 + g178 x160 + g103 x144 + g97 x136 + g37 x132 + g172 x130 + g102 x129 + g62 x96 + g145 x80 + g96 x72 + g132 x68 + g210 x66 + g69 x65 + g69 x48 + g11 x40 + x36 + g4 x34 + g76 x33 + g122 x24 + g6 x20 + g145 x18 + g155 x17 + g41 x12 + g40 x10 + g106 x9 + g144 x6 + g102 x5 + g246 x3
g22 x192 + g167 x160 + g178 x144 + g84 x136 + g219 x132 + g248 x130 + g130 x129 + g221 x96 + g84 x80 + g123 x72 + g140 x68 + g26 x66 + g108 x65 + g50 x48 + g15 x40 + g211 x36 + g116 x34 + g19 x33 + g228 x24 + g176 x20 + g42 x18 + g80 x17 + g180 x12 + g203 x10 + g104 x9 + g72 x6 + g151 x5 + g247 x3
g156 x192 + g25 x160 + g158 x144 + g20 x136 + g50 x132 + g140 x130 + g203 x129 + g184 x96 + g152 x80 + g228 x72 + g194 x68 + g203 x66 + g131 x65 + g25 x48 + g192 x40 + g191 x36 + g125 x34 + g136 x33 + g132 x24 + g85 x20 + g191 x18 + g120 x17 + g212 x12 + g244 x10 + g133 x9 + g78 x6 + g161 x5 + g x3
g193 x192 + g33 x160 + g22 x144 + g204 x136 + g173 x132 + g50 x130 + g66 x129 + g42 x96 + g69 x80 + g175 x72 + g230 x68 + g253 x66 + g16 x65 + g52 x48 + g54 x40 + g9 x36 + g177 x34 + g99 x33 + g12 x24 + g37 x20 + g83 x18 + g230 x17 + g78 x12 + g x10 + g64 x9 + g225 x6 + g68 x5 + g204 x3
g88 x192 + g8 x160 + g11 x144 + g121 x136 + g205 x132 + g165 x130 + g206 x129 + g164 x96 + g235 x80 + g94 x72 + g173 x68 + g142 x66 + g238 x65 + g102 x48 + g113 x40 + g183 x36 + g187 x34 + g157 x33 + g2 x24 + g23 x20 + g122 x18 + g21 x17 + g154 x12 + g78 x10 + g117 x9 + g177 x6 + g111 x5 + g60 x3
g212 x192 + g198 x160 + g175 x144 + g80 x136 + g196 x132 + g167 x130 + g2 x129 + g65 x96 + g243 x80 + g91 x72 + g171 x68 + g211 x66 + g182 x65 + g247 x48 + g86 x40 + g89 x36 + g87 x34 + g83 x33 + g138 x24 + g45 x20 + g149 x18 + g100 x17 + g188 x12 + g17 x10 + g243 x9 + g237 x6 + g112 x5 + g137 x3
g117 x192 + g61 x160 + g230 x144 + g105 x136 + g191 x132 + g113 x130 + g245 x129 + g139 x96 + g166 x80 + g210 x72 + g221 x68 + g138 x66 + g146 x65 + g120 x48 + g124 x40 + g252 x36 + g182 x34 + g5 x33 + g8 x24 + g136 x20 + g235 x18 + g61 x17 + g45 x12 + g149 x10 + g158 x9 + g13 x6 + g169 x5 + g121 x3
g34 x192 + g57 x160 + g187 x144 + g36 x136 + g137 x132 + g63 x130 + g98 x129 + g236 x96 + g161 x80 + g66 x72 + g191 x68 + g117 x66 + g241 x65 + g7 x48 + g9 x40 + g153 x36 + g118 x34 + g154 x33 + g194 x24 + g157 x20 + g14 x18 + g116 x17 + g119 x12 + g113 x10 + g13 x9 + g138 x6 + g143 x5 + g35 x3
g140 x192 + g233 x160 + g150 x144 + g146 x136 + g99 x132 + g249 x130 + g211 x129 + g66 x96 + g37 x80 + g35 x72 + g199 x68 + g170 x66 + g2 x65 + g217 x48 + g2 x40 + g192 x36 + g32 x34 + g229 x33 + g241 x24 + g200 x20 + g63 x18 + g17 x17 + g251 x12 + g44 x10 + g106 x9 + g25 x6 + g174 x5 + g127 x3
g237 x192 + g133 x160 + g204 x144 + g169 x136 + g30 x132 + g127 x130 + g41 x129 + g12 x96 + g198 x80 + g151 x72 + g252 x68 + g29 x66 + g144 x65 + g120 x48 + g72 x40 + g123 x36 + g170 x34 + g159 x33 + g77 x24 + g227 x20 + g161 x18 + g231 x17 + g159 x12 + g253 x10 + g56 x9 + g35 x6 + g251 x5 + g99 x3