Information on Result #606336
Linear OA(53, 5, F5, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,5) or 5-cap in PG(2,5)), using Reed–Solomon code RS(2,5)
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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(539, 45, F5, 27) (dual of [45, 6, 28]-code) | [i] | Concatenation of Two Codes | |
| 2 | Linear OA(544, 50, F5, 31) (dual of [50, 6, 32]-code) | [i] | ||
| 3 | Linear OA(549, 55, F5, 35) (dual of [55, 6, 36]-code) | [i] | ||
| 4 | Linear OA(557, 65, F5, 39) (dual of [65, 8, 40]-code) | [i] | ||
| 5 | Linear OA(554, 60, F5, 39) (dual of [60, 6, 40]-code) | [i] | ||
| 6 | Linear OA(562, 70, F5, 43) (dual of [70, 8, 44]-code) | [i] | ||
| 7 | Linear OA(559, 65, F5, 43) (dual of [65, 6, 44]-code) | [i] | ||
| 8 | Linear OA(567, 75, F5, 47) (dual of [75, 8, 48]-code) | [i] | ||
| 9 | Linear OA(564, 70, F5, 47) (dual of [70, 6, 48]-code) | [i] | ||
| 10 | Linear OA(575, 85, F5, 51) (dual of [85, 10, 52]-code) | [i] | ||
| 11 | Linear OA(572, 80, F5, 51) (dual of [80, 8, 52]-code) | [i] | ||
| 12 | Linear OA(569, 75, F5, 51) (dual of [75, 6, 52]-code) | [i] | ||
| 13 | Linear OA(580, 90, F5, 55) (dual of [90, 10, 56]-code) | [i] | ||
| 14 | Linear OA(577, 85, F5, 55) (dual of [85, 8, 56]-code) | [i] | ||
| 15 | Linear OA(574, 80, F5, 55) (dual of [80, 6, 56]-code) | [i] | ||
| 16 | Linear OA(594, 110, F5, 59) (dual of [110, 16, 60]-code) | [i] | ||
| 17 | Linear OA(585, 95, F5, 59) (dual of [95, 10, 60]-code) | [i] | ||
| 18 | Linear OA(582, 90, F5, 59) (dual of [90, 8, 60]-code) | [i] | ||
| 19 | Linear OA(579, 85, F5, 59) (dual of [85, 6, 60]-code) | [i] | ||
| 20 | Linear OA(596, 110, F5, 63) (dual of [110, 14, 64]-code) | [i] | ||
| 21 | Linear OA(593, 105, F5, 63) (dual of [105, 12, 64]-code) | [i] | ||
| 22 | Linear OA(590, 100, F5, 63) (dual of [100, 10, 64]-code) | [i] | ||
| 23 | Linear OA(581, 85, F5, 63) (dual of [85, 4, 64]-code) | [i] | ||
| 24 | Linear OA(5101, 115, F5, 67) (dual of [115, 14, 68]-code) | [i] | ||
| 25 | Linear OA(598, 110, F5, 67) (dual of [110, 12, 68]-code) | [i] | ||
| 26 | Linear OA(595, 105, F5, 67) (dual of [105, 10, 68]-code) | [i] | ||
| 27 | Linear OA(586, 90, F5, 67) (dual of [90, 4, 68]-code) | [i] | ||
| 28 | Linear OA(5112, 130, F5, 71) (dual of [130, 18, 72]-code) | [i] | ||
| 29 | Linear OA(5109, 125, F5, 71) (dual of [125, 16, 72]-code) | [i] | ||
| 30 | Linear OA(5106, 120, F5, 71) (dual of [120, 14, 72]-code) | [i] | ||
| 31 | Linear OA(5103, 115, F5, 71) (dual of [115, 12, 72]-code) | [i] | ||
| 32 | Linear OA(5100, 110, F5, 71) (dual of [110, 10, 72]-code) | [i] | ||
| 33 | Linear OA(591, 95, F5, 71) (dual of [95, 4, 72]-code) | [i] | ||
| 34 | Linear OA(5114, 130, F5, 75) (dual of [130, 16, 76]-code) | [i] | ||
| 35 | Linear OA(5111, 125, F5, 75) (dual of [125, 14, 76]-code) | [i] | ||
| 36 | Linear OA(5108, 120, F5, 75) (dual of [120, 12, 76]-code) | [i] | ||
| 37 | Linear OA(5105, 115, F5, 75) (dual of [115, 10, 76]-code) | [i] | ||
| 38 | Linear OA(5116, 130, F5, 79) (dual of [130, 14, 80]-code) | [i] | ||
| 39 | Linear OA(5113, 125, F5, 79) (dual of [125, 12, 80]-code) | [i] | ||
| 40 | Linear OA(5110, 120, F5, 79) (dual of [120, 10, 80]-code) | [i] | ||
| 41 | Linear OA(5118, 130, F5, 83) (dual of [130, 12, 84]-code) | [i] | ||
| 42 | Linear OA(5115, 125, F5, 83) (dual of [125, 10, 84]-code) | [i] | ||
| 43 | Linear OA(5120, 130, F5, 87) (dual of [130, 10, 88]-code) | [i] | ||
| 44 | Linear OA(5124, 130, F5, 95) (dual of [130, 6, 96]-code) | [i] | ||
| 45 | Linear OA(5118, 140, F5, 67) (dual of [140, 22, 68]-code) | [i] | ||
| 46 | Linear OA(5123, 145, F5, 71) (dual of [145, 22, 72]-code) | [i] | ||
| 47 | Linear OA(5120, 140, F5, 71) (dual of [140, 20, 72]-code) | [i] | ||
| 48 | Linear OA(5125, 145, F5, 75) (dual of [145, 20, 76]-code) | [i] | ||
| 49 | Linear OA(5143, 165, F5, 87) (dual of [165, 22, 88]-code) | [i] | ||
| 50 | Linear OA(5140, 160, F5, 87) (dual of [160, 20, 88]-code) | [i] | ||
| 51 | Linear OA(5148, 170, F5, 91) (dual of [170, 22, 92]-code) | [i] | ||
| 52 | Linear OA(5145, 165, F5, 91) (dual of [165, 20, 92]-code) | [i] | ||
| 53 | Linear OA(5142, 160, F5, 91) (dual of [160, 18, 92]-code) | [i] | ||
| 54 | Linear OA(5150, 170, F5, 95) (dual of [170, 20, 96]-code) | [i] | ||
| 55 | Linear OA(5147, 165, F5, 95) (dual of [165, 18, 96]-code) | [i] | ||
| 56 | Linear OA(5144, 160, F5, 95) (dual of [160, 16, 96]-code) | [i] | ||
| 57 | Linear OA(5149, 165, F5, 99) (dual of [165, 16, 100]-code) | [i] | ||
| 58 | Linear OOA(5150, 85, F5, 2, 99) (dual of [(85, 2), 20, 100]-NRT-code) | [i] | Concatenation of Two NRT-Codes | |
| 59 | Linear OOA(5148, 80, F5, 2, 107) (dual of [(80, 2), 12, 108]-NRT-code) | [i] | ||
| 60 | Linear OA(597, 161, F5, 42) (dual of [161, 64, 43]-code) | [i] | Construction X with Cyclic Codes | |
| 61 | Linear OA(525, 35, F5, 15) (dual of [35, 10, 16]-code) | [i] | Construction XX with Cyclic Codes | |
| 62 | Linear OA(529, 40, F5, 17) (dual of [40, 11, 18]-code) | [i] | ||
| 63 | Linear OA(528, 38, F5, 17) (dual of [38, 10, 18]-code) | [i] | ||
| 64 | Linear OA(5143, 642, F5, 43) (dual of [642, 499, 44]-code) | [i] | Construction XX with a Chain of Cyclic Codes | |
| 65 | Linear OA(5122, 653, F5, 35) (dual of [653, 531, 36]-code) | [i] | ||
| 66 | Linear OA(5111, 642, F5, 33) (dual of [642, 531, 34]-code) | [i] | ||
| 67 | Linear OA(590, 653, F5, 25) (dual of [653, 563, 26]-code) | [i] | ||
| 68 | Linear OA(579, 642, F5, 23) (dual of [642, 563, 24]-code) | [i] | ||
| 69 | Linear OA(547, 642, F5, 13) (dual of [642, 595, 14]-code) | [i] | ||
| 70 | Linear OA(5137, 159, F5, 80) (dual of [159, 22, 81]-code) | [i] | Construction XX with a Chain of Extended Narrow-Sense BCH Codes | |
| 71 | Linear OA(5126, 148, F5, 74) (dual of [148, 22, 75]-code) | [i] | ||
| 72 | Linear OA(5122, 144, F5, 73) (dual of [144, 22, 74]-code) | [i] | ||
| 73 | Linear OA(5120, 142, F5, 72) (dual of [142, 22, 73]-code) | [i] | ||
| 74 | Linear OA(5117, 139, F5, 70) (dual of [139, 22, 71]-code) | [i] | ||
| 75 | Linear OA(520, 37, F5, 11) (dual of [37, 17, 12]-code) | [i] | Construction X with Varšamov Bound | |
| 76 | Linear OA(552, 69, F5, 30) (dual of [69, 17, 31]-code) | [i] | ||
| 77 | Linear OA(561, 78, F5, 36) (dual of [78, 17, 37]-code) | [i] | ||
| 78 | Linear OA(565, 131, F5, 30) (dual of [131, 66, 31]-code) | [i] | ||
| 79 | Linear OA(566, 132, F5, 31) (dual of [132, 66, 32]-code) | [i] | ||
| 80 | Linear OA(570, 135, F5, 33) (dual of [135, 65, 34]-code) | [i] | ||
| 81 | Linear OA(592, 121, F5, 51) (dual of [121, 29, 52]-code) | [i] | ||
| 82 | Linear OA(593, 122, F5, 52) (dual of [122, 29, 53]-code) | [i] | ||
| 83 | Linear OA(5119, 147, F5, 69) (dual of [147, 28, 70]-code) | [i] | ||
| 84 | Linear OA(5131, 151, F5, 80) (dual of [151, 20, 81]-code) | [i] | ||
| 85 | Linear OA(535, 68, F5, 18) (dual of [68, 33, 19]-code) | [i] | ||
| 86 | Linear OA(549, 74, F5, 26) (dual of [74, 25, 27]-code) | [i] | ||
| 87 | Linear OA(550, 75, F5, 27) (dual of [75, 25, 28]-code) | [i] | ||
| 88 | Linear OA(564, 94, F5, 34) (dual of [94, 30, 35]-code) | [i] | ||
| 89 | Linear OA(578, 105, F5, 43) (dual of [105, 27, 44]-code) | [i] | ||
| 90 | Linear OA(579, 106, F5, 44) (dual of [106, 27, 45]-code) | [i] | ||
| 91 | Linear OA(581, 109, F5, 45) (dual of [109, 28, 46]-code) | [i] | ||
| 92 | Linear OA(5111, 140, F5, 64) (dual of [140, 29, 65]-code) | [i] | Construction X with Varšamov–Edel Bound | |