Information on Result #658598

Linear OA(1661, 64, F16, 58) (dual of [64, 3, 59]-code), using algebraic-geometric code AG(F,5P) with known gap numbers based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using the Hermitian function field over F16 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(1661, 64, F16, 57) (dual of [64, 3, 58]-code) [i]Strength Reduction
2Linear OA(16125, 128, F16, 117) (dual of [128, 3, 118]-code) [i]Repeating Each Code Word
3Linear OA(1663, 67, F16, 58) (dual of [67, 4, 59]-code) [i]✔Construction X with Algebraic-Geometric Codes
4Linear OA(1664, 69, F16, 58) (dual of [69, 5, 59]-code) [i]✔
5Linear OA(1665, 71, F16, 58) (dual of [71, 6, 59]-code) [i]✔
6Linear OA(1667, 74, F16, 58) (dual of [74, 7, 59]-code) [i]✔
7Linear OA(1668, 76, F16, 58) (dual of [76, 8, 59]-code) [i]✔
8Linear OA(1669, 78, F16, 58) (dual of [78, 9, 59]-code) [i]✔
9Linear OA(1670, 80, F16, 58) (dual of [80, 10, 59]-code) [i]✔
10Linear OA(1672, 83, F16, 58) (dual of [83, 11, 59]-code) [i]✔
11Linear OA(1670, 81, F16, 57) (dual of [81, 11, 58]-code) [i]✔
12Linear OA(1673, 85, F16, 58) (dual of [85, 12, 59]-code) [i]✔
13Linear OA(1674, 87, F16, 58) (dual of [87, 13, 59]-code) [i]✔
14Linear OA(1676, 90, F16, 58) (dual of [90, 14, 59]-code) [i]✔
15Linear OA(1674, 88, F16, 57) (dual of [88, 14, 58]-code) [i]✔
16Linear OA(1677, 92, F16, 58) (dual of [92, 15, 59]-code) [i]✔
17Linear OA(1678, 94, F16, 58) (dual of [94, 16, 59]-code) [i]✔
18Linear OA(1679, 96, F16, 58) (dual of [96, 17, 59]-code) [i]✔
19Linear OA(1681, 99, F16, 58) (dual of [99, 18, 59]-code) [i]✔
20Linear OA(1679, 97, F16, 57) (dual of [97, 18, 58]-code) [i]✔
21Linear OA(1682, 101, F16, 58) (dual of [101, 19, 59]-code) [i]✔
22Linear OA(1684, 104, F16, 58) (dual of [104, 20, 59]-code) [i]✔
23Linear OA(1682, 102, F16, 57) (dual of [102, 20, 58]-code) [i]✔
24Linear OA(1685, 106, F16, 58) (dual of [106, 21, 59]-code) [i]✔
25Linear OA(1686, 108, F16, 58) (dual of [108, 22, 59]-code) [i]✔
26Linear OA(1688, 111, F16, 58) (dual of [111, 23, 59]-code) [i]✔
27Linear OA(1686, 109, F16, 57) (dual of [109, 23, 58]-code) [i]✔
28Linear OA(1689, 113, F16, 58) (dual of [113, 24, 59]-code) [i]✔
29Linear OA(1691, 116, F16, 58) (dual of [116, 25, 59]-code) [i]✔
30Linear OA(1688, 113, F16, 56) (dual of [113, 25, 57]-code) [i]✔
31Linear OA(1692, 118, F16, 58) (dual of [118, 26, 59]-code) [i]✔
32Linear OA(1693, 120, F16, 58) (dual of [120, 27, 59]-code) [i]✔
33Linear OA(1694, 122, F16, 58) (dual of [122, 28, 59]-code) [i]✔
34Linear OA(1695, 124, F16, 58) (dual of [124, 29, 59]-code) [i]✔
35Linear OA(1696, 126, F16, 58) (dual of [126, 30, 59]-code) [i]✔
36Linear OA(1697, 128, F16, 58) (dual of [128, 31, 59]-code) [i]✔
37Linear OA(1671, 82, F16, 58) (dual of [82, 11, 59]-code) [i]✔Construction XX with a Chain of Algebraic-Geometric Codes
38Linear OA(1670, 82, F16, 56) (dual of [82, 12, 57]-code) [i]✔
39Linear OA(1675, 89, F16, 58) (dual of [89, 14, 59]-code) [i]✔
40Linear OA(1674, 89, F16, 56) (dual of [89, 15, 57]-code) [i]✔
41Linear OOA(1661, 32, F16, 2, 58) (dual of [(32, 2), 3, 59]-NRT-code) [i]OOA Folding