Mathematical Problems in Engineering

Research Article

More Low Differential Uniformity Permutations over with Odd

Table 1

CCZ-inequivalent differential 4-uniformity permutations in Theorem 2 over with .
No.NLExtend Walsh spectrumDifferential spectrum
122{0 [783], 4 [1206], 8 [1024], 12 [798], 16 [209], 20 [12]}{0 [2127], 2 [1794], 4 [111]}
222{0 [795], 4 [1210], 8 [1008], 12 [792], 16 [213], 20 [14]}{0 [2139], 2 [1770], 4 [123]}
322{0 [794], 4 [1236], 8 [1012], 12 [751], 16 [210], 20 [29]}{0 [2181], 2 [1686], 4 [165]}
420{0 [805], 4 [1214], 8 [1014], 12 [774], 16 [195], 20 [28], 24 [2]}{0 [2181], 2 [1686], 4 [165]}
520{0 [797], 4 [1240], 8 [998], 12 [755], 16 [219], 20 [21], 24 [2]}{0 [2181], 2 [1686], 4 [165]}
620{..0 [799], 4 [1242], 8 [999], 12 [748], 16 [217], 20 [26], 24 [1]}{0 [2187], 2 [1674], 4 [171]}
720{0 [813], 4 [1244], 8 [991], 12 [737], 16 [211], 20 [35], 24 [1]}{0 [2211], 2 [1626], 4 [195]}
820{0 [790], 4 [1252], 8 [1017], 12 [731], 16 [206], 20 [33], 24 [3]}{0 [2211], 2 [1626], 4 [195]}
920{0 [804], 4 [1254], 8 [991], 12 [736], 16 [216], 20 [26], 24 [5]}{0 [2217], 2 [1614], 4 [201]}
1018{0 [841], 4 [1216], 8 [966], 12 [774], 16 [207], 20 [24], 24 [2], 28 [2]}{0 [2217], 2 [1614], 4 [201]}
1120{0 [810], 4 [1242], 8 [999], 12 [742], 16 [202], 20 [32], 24 [5]}{0 [2223], 2 [1602], 4 [207]}
1220{0 [831], 4 [1230], 8 [981], 12 [750], 16 [201], 20 [36], 24 [3]}{0 [2223], 2 [1602], 4 [207]}
1320{0 [803], 4 [1264], 8 [988], 12 [723], 16 [221], 20 [29], 24 [4]}{0 [2223], 2 [1602], 4 [207]}
1418{0 [808], 4 [1262], 8 [993], 12 [716], 16 [212], 20 [38], 24 [3]}{0 [2235], 2 [1578], 4 [219]}
1520{0 [815], 4 [1262], 8 [997], 12 [726], 16 [217], 20 [28], 24 [7]}{0 [2241], 2 [1566], 4 [225]}
1618{0 [815], 4 [1255], 8 [990], 12 [722], 16 [209], 20 [38], 24 [2], 28 [1]}{0 [2241], 2 [1566], 4 [225]}
1718{0 [822], 4 [1240], 8 [983], 12 [748], 16 [206], 20 [26], 24 [5], 28 [2]}{0 [2241], 2 [1566], 4 [225]}
1820{0 [801], 4 [1258], 8 [1008], 12 [724], 16 [199], 20 [34], 24 [8]}{0 [2247], 2 [1554], 4 [231]}
1920{0 [801], 4 [1278], 8 [994], 12 [702], 16 [215], 20 [36], 24 [6]}{0 [2253], 2 [1542], 4 [237]}
2018{0 [816], 4 [1265], 8 [971], 12 [729], 16 [220], 20 [21], 24 [9], 28 [1]}{0 [2253], 2 [1542], 4 [237]}
2120{0 [803], 4 [1286], 8 [986], 12 [694], 16 [221], 20 [36], 24 [6]}{0 [2259], 2 [1530], 4 [243]}
2218{0 [820], 4 [1257], 8 [980], 12 [729], 16 [208], 20 [29], 24 [8], 28 [1]}{0 [2259], 2 [1530], 4 [243]}
2318{0 [801], 4 [1276], 8 [994], 12 [708], 16 [215], 20 [30], 24 [6], 28 [2]}{0 [2259], 2 [1530], 4 [249]}
2418{0 [805], 4 [1266], 8 [996], 12 [718], 16 [211], 20 [28], 24 [4], 28 [4]}{0 [2271], 2 [1506], 4 [255]}
2522{0 [795], 4 [1302], 8 [1008], 12 [654], 16 [213], 20 [60]}{0 [2277], 2 [1494], 4 [261]}
2618{0 [795], 4 [1284], 8 [1000], 12 [700], 16 [213], 20 [30], 24 [8], 28 [2]}{0 [2277], 2 [1494], 4 [261]}
2720{0 [783], 4 [1302], 8 [1012], 12 [678], 16 [209], 20 [36], 24 [12]}{0 [2289], 2 [1470], 4 [273]}