Information on Result #606796
Linear OA(53, 6, F5, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,5) or 6-cap in PG(2,5)), using extended Reed–Solomon code RSe(3,5)
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
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(513, 31, F5, 7) (dual of [31, 18, 8]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(519, 131, F5, 7) (dual of [131, 112, 8]-code) | [i] | ||
| 3 | Linear OA(524, 631, F5, 7) (dual of [631, 607, 8]-code) | [i] | ||
| 4 | Linear OA(529, 3131, F5, 7) (dual of [3131, 3102, 8]-code) | [i] | ||
| 5 | Linear OA(534, 15631, F5, 7) (dual of [15631, 15597, 8]-code) | [i] | ||
| 6 | Linear OA(539, 78131, F5, 7) (dual of [78131, 78092, 8]-code) | [i] | ||
| 7 | Linear OA(544, 390631, F5, 7) (dual of [390631, 390587, 8]-code) | [i] | ||
| 8 | Linear OA(549, 1953131, F5, 7) (dual of [1953131, 1953082, 8]-code) | [i] | ||
| 9 | Linear OA(528, 15631, F5, 6) (dual of [15631, 15603, 7]-code) | [i] | ||
| 10 | Linear OA(532, 78131, F5, 6) (dual of [78131, 78099, 7]-code) | [i] | ||
| 11 | Linear OA(536, 390631, F5, 6) (dual of [390631, 390595, 7]-code) | [i] | ||
| 12 | Linear OA(540, 1953131, F5, 6) (dual of [1953131, 1953091, 7]-code) | [i] | ||
| 13 | Linear OA(521, 30, F5, 14) (dual of [30, 9, 15]-code) | [i] | Generalized (u, u+v)-Construction | |
| 14 | Linear OA(524, 34, F5, 14) (dual of [34, 10, 15]-code) | [i] | ||
| 15 | Linear OA(525, 36, F5, 14) (dual of [36, 11, 15]-code) | [i] | ||
| 16 | Linear OA(513, 30, F5, 7) (dual of [30, 17, 8]-code) | [i] | ||
| 17 | Linear OA(5148, 1953132, F5, 21) (dual of [1953132, 1952984, 22]-code) | [i] | Construction X with Cyclic Codes | |
| 18 | Linear OA(576, 1953132, F5, 11) (dual of [1953132, 1953056, 12]-code) | [i] | ||
| 19 | Linear OA(5132, 390632, F5, 21) (dual of [390632, 390500, 22]-code) | [i] | ||
| 20 | Linear OA(568, 390632, F5, 11) (dual of [390632, 390564, 12]-code) | [i] | ||
| 21 | Linear OA(5116, 78132, F5, 21) (dual of [78132, 78016, 22]-code) | [i] | ||
| 22 | Linear OA(560, 78132, F5, 11) (dual of [78132, 78072, 12]-code) | [i] | ||
| 23 | Linear OA(5148, 15632, F5, 31) (dual of [15632, 15484, 32]-code) | [i] | ||
| 24 | Linear OA(5100, 15632, F5, 21) (dual of [15632, 15532, 22]-code) | [i] | ||
| 25 | Linear OA(552, 15632, F5, 11) (dual of [15632, 15580, 12]-code) | [i] | ||
| 26 | Linear OA(5124, 3132, F5, 31) (dual of [3132, 3008, 32]-code) | [i] | ||
| 27 | Linear OA(584, 3132, F5, 21) (dual of [3132, 3048, 22]-code) | [i] | ||
| 28 | Linear OA(544, 3132, F5, 11) (dual of [3132, 3088, 12]-code) | [i] | ||
| 29 | Linear OA(5132, 632, F5, 41) (dual of [632, 500, 42]-code) | [i] | ||
| 30 | Linear OA(5100, 632, F5, 31) (dual of [632, 532, 32]-code) | [i] | ||
| 31 | Linear OA(568, 632, F5, 21) (dual of [632, 564, 22]-code) | [i] | ||
| 32 | Linear OA(536, 632, F5, 11) (dual of [632, 596, 12]-code) | [i] | ||
| 33 | Linear OA(5124, 319, F5, 41) (dual of [319, 195, 42]-code) | [i] | ||
| 34 | Linear OA(592, 319, F5, 31) (dual of [319, 227, 32]-code) | [i] | ||
| 35 | Linear OA(528, 132, F5, 11) (dual of [132, 104, 12]-code) | [i] | ||
| 36 | Linear OA(527, 37, F5, 16) (dual of [37, 10, 17]-code) | [i] | ||
| 37 | Linear OA(533, 40, F5, 22) (dual of [40, 7, 23]-code) | [i] | Construction XX with Cyclic Codes | |
| 38 | Linear OA(523, 34, F5, 14) (dual of [34, 11, 15]-code) | [i] | ||
| 39 | Linear OA(522, 32, F5, 14) (dual of [32, 10, 15]-code) | [i] | ||
| 40 | Linear OA(538, 73, F5, 17) (dual of [73, 35, 18]-code) | [i] | ||
| 41 | Linear OA(537, 71, F5, 17) (dual of [71, 34, 18]-code) | [i] | ||
| 42 | Linear OA(577, 133, F5, 38) (dual of [133, 56, 39]-code) | [i] | ||
| 43 | Linear OA(581, 137, F5, 39) (dual of [137, 56, 40]-code) | [i] | ||
| 44 | Linear OA(586, 133, F5, 43) (dual of [133, 47, 44]-code) | [i] | ||
| 45 | Linear OA(590, 137, F5, 44) (dual of [137, 47, 45]-code) | [i] | ||
| 46 | Linear OA(595, 133, F5, 48) (dual of [133, 38, 49]-code) | [i] | ||
| 47 | Linear OA(599, 137, F5, 49) (dual of [137, 38, 50]-code) | [i] | ||
| 48 | Linear OA(5112, 135, F5, 69) (dual of [135, 23, 70]-code) | [i] | ||
| 49 | Linear OA(5111, 133, F5, 69) (dual of [133, 22, 70]-code) | [i] | ||
| 50 | Linear OA(5121, 144, F5, 73) (dual of [144, 23, 74]-code) | [i] | ||
| 51 | Linear OA(5118, 141, F5, 71) (dual of [141, 23, 72]-code) | [i] | ||
| 52 | Linear OA(5120, 142, F5, 73) (dual of [142, 22, 74]-code) | [i] | ||
| 53 | Linear OA(5126, 149, F5, 74) (dual of [149, 23, 75]-code) | [i] | ||
| 54 | Linear OA(5134, 157, F5, 78) (dual of [157, 23, 79]-code) | [i] | ||
| 55 | Linear OA(5130, 153, F5, 75) (dual of [153, 23, 76]-code) | [i] | ||
| 56 | Linear OA(5119, 141, F5, 73) (dual of [141, 22, 74]-code) | [i] | ||
| 57 | Linear OA(5115, 137, F5, 70) (dual of [137, 22, 71]-code) | [i] | ||
| 58 | Linear OA(5124, 146, F5, 74) (dual of [146, 22, 75]-code) | [i] | ||
| 59 | Linear OA(5130, 152, F5, 76) (dual of [152, 22, 77]-code) | [i] | ||
| 60 | Linear OA(5118, 135, F5, 74) (dual of [135, 17, 75]-code) | [i] | ||
| 61 | Linear OA(5150, 3158, F5, 34) (dual of [3158, 3008, 35]-code) | [i] | Construction XX with a Chain of Cyclic Codes | |
| 62 | Linear OA(5112, 3160, F5, 25) (dual of [3160, 3048, 26]-code) | [i] | ||
| 63 | Linear OA(5110, 3158, F5, 24) (dual of [3158, 3048, 25]-code) | [i] | ||
| 64 | Linear OA(5123, 655, F5, 35) (dual of [655, 532, 36]-code) | [i] | ||
| 65 | Linear OA(591, 655, F5, 25) (dual of [655, 564, 26]-code) | [i] | ||
| 66 | Linear OA(5122, 319, F5, 41) (dual of [319, 197, 42]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 67 | Linear OA(5124, 131, F5, 98) (dual of [131, 7, 99]-code) | [i] | ||
| 68 | Linear OA(5114, 131, F5, 73) (dual of [131, 17, 74]-code) | [i] | ||
| 69 | Linear OA(5108, 131, F5, 68) (dual of [131, 23, 69]-code) | [i] | ||
| 70 | Linear OA(5101, 131, F5, 53) (dual of [131, 30, 54]-code) | [i] | ||
| 71 | Linear OA(534, 69, F5, 16) (dual of [69, 35, 17]-code) | [i] | ||
| 72 | Linear OA(520, 31, F5, 13) (dual of [31, 11, 14]-code) | [i] | ||
| 73 | Linear OA(5138, 161, F5, 80) (dual of [161, 23, 81]-code) | [i] | Construction XX with a Chain of Extended Narrow-Sense BCH Codes | |
| 74 | Linear OA(5114, 143, F5, 63) (dual of [143, 29, 64]-code) | [i] | ||
| 75 | Linear OA(531, 37, F5, 23) (dual of [37, 6, 24]-code) | [i] | Construction X with De Boer–Brouwer Codes | |
| 76 | Linear OA(566, 133, F5, 30) (dual of [133, 67, 31]-code) | [i] | Construction X with Varšamov Bound | |
| 77 | Linear OA(567, 134, F5, 31) (dual of [134, 67, 32]-code) | [i] | ||
| 78 | Linear OA(569, 136, F5, 32) (dual of [136, 67, 33]-code) | [i] | ||
| 79 | Linear OA(571, 137, F5, 33) (dual of [137, 66, 34]-code) | [i] | ||
| 80 | Linear OA(572, 139, F5, 33) (dual of [139, 67, 34]-code) | [i] | ||
| 81 | Linear OA(574, 139, F5, 34) (dual of [139, 65, 35]-code) | [i] | ||
| 82 | Linear OA(594, 124, F5, 52) (dual of [124, 30, 53]-code) | [i] | ||
| 83 | Linear OA(596, 126, F5, 53) (dual of [126, 30, 54]-code) | [i] | ||
| 84 | Linear OA(599, 129, F5, 55) (dual of [129, 30, 56]-code) | [i] | ||
| 85 | Linear OA(5118, 148, F5, 67) (dual of [148, 30, 68]-code) | [i] | ||
| 86 | Linear OA(551, 77, F5, 27) (dual of [77, 26, 28]-code) | [i] | ||
| 87 | Linear OA(543, 82, F5, 21) (dual of [82, 39, 22]-code) | [i] | ||
| 88 | Linear OA(565, 96, F5, 34) (dual of [96, 31, 35]-code) | [i] | ||
| 89 | Linear OA(580, 108, F5, 44) (dual of [108, 28, 45]-code) | [i] | ||
| 90 | Linear OA(528, 32, F5, 23) (dual of [32, 4, 24]-code) | [i] | Construction X with Ovoid | |