Information on Result #609783
Linear OA(55, 42, F5, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,5)), using large caps in PG(4, b)
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(5150, 1953167, F5, 19) (dual of [1953167, 1953017, 20]-code) | [i] | Construction X with Cyclic Codes | |
| 2 | Linear OA(5114, 1953167, F5, 15) (dual of [1953167, 1953053, 16]-code) | [i] | ||
| 3 | Linear OA(5134, 390663, F5, 19) (dual of [390663, 390529, 20]-code) | [i] | ||
| 4 | Linear OA(5102, 390663, F5, 15) (dual of [390663, 390561, 16]-code) | [i] | ||
| 5 | Linear OA(5146, 78159, F5, 25) (dual of [78159, 78013, 26]-code) | [i] | ||
| 6 | Linear OA(5118, 78159, F5, 19) (dual of [78159, 78041, 20]-code) | [i] | ||
| 7 | Linear OA(5104, 78159, F5, 17) (dual of [78159, 78055, 18]-code) | [i] | ||
| 8 | Linear OA(590, 78159, F5, 15) (dual of [78159, 78069, 16]-code) | [i] | ||
| 9 | Linear OA(5150, 15655, F5, 29) (dual of [15655, 15505, 30]-code) | [i] | ||
| 10 | Linear OA(5138, 15655, F5, 27) (dual of [15655, 15517, 28]-code) | [i] | ||
| 11 | Linear OA(5126, 15655, F5, 25) (dual of [15655, 15529, 26]-code) | [i] | ||
| 12 | Linear OA(5102, 15655, F5, 19) (dual of [15655, 15553, 20]-code) | [i] | ||
| 13 | Linear OA(590, 15655, F5, 17) (dual of [15655, 15565, 18]-code) | [i] | ||
| 14 | Linear OA(578, 15655, F5, 15) (dual of [15655, 15577, 16]-code) | [i] | ||
| 15 | Linear OA(5130, 3158, F5, 29) (dual of [3158, 3028, 30]-code) | [i] | Construction XX with a Chain of Cyclic Codes | |
| 16 | Linear OA(5120, 3158, F5, 27) (dual of [3158, 3038, 28]-code) | [i] | ||
| 17 | Linear OA(5114, 3163, F5, 25) (dual of [3163, 3049, 26]-code) | [i] | ||
| 18 | Linear OA(5112, 3160, F5, 25) (dual of [3160, 3048, 26]-code) | [i] | ||
| 19 | Linear OA(5150, 1953157, F5, 21) (dual of [1953157, 1953007, 22]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 20 | Linear OA(5132, 1953157, F5, 18) (dual of [1953157, 1953025, 19]-code) | [i] | ||
| 21 | Linear OA(5123, 1953157, F5, 17) (dual of [1953157, 1953034, 18]-code) | [i] | ||
| 22 | Linear OA(5114, 1953157, F5, 16) (dual of [1953157, 1953043, 17]-code) | [i] | ||
| 23 | Linear OA(596, 1953157, F5, 13) (dual of [1953157, 1953061, 14]-code) | [i] | ||
| 24 | Linear OA(587, 1953157, F5, 12) (dual of [1953157, 1953070, 13]-code) | [i] | ||
| 25 | Linear OA(578, 1953157, F5, 11) (dual of [1953157, 1953079, 12]-code) | [i] | ||
| 26 | Linear OA(560, 1953157, F5, 8) (dual of [1953157, 1953097, 9]-code) | [i] | ||
| 27 | Linear OA(5150, 1953166, F5, 20) (dual of [1953166, 1953016, 21]-code) | [i] | ||
| 28 | Linear OA(578, 1953166, F5, 10) (dual of [1953166, 1953088, 11]-code) | [i] | ||
| 29 | Linear OA(5150, 390654, F5, 23) (dual of [390654, 390504, 24]-code) | [i] | ||
| 30 | Linear OA(5142, 390654, F5, 22) (dual of [390654, 390512, 23]-code) | [i] | ||
| 31 | Linear OA(5134, 390654, F5, 21) (dual of [390654, 390520, 22]-code) | [i] | ||
| 32 | Linear OA(5118, 390654, F5, 18) (dual of [390654, 390536, 19]-code) | [i] | ||
| 33 | Linear OA(5110, 390654, F5, 17) (dual of [390654, 390544, 18]-code) | [i] | ||
| 34 | Linear OA(5102, 390654, F5, 16) (dual of [390654, 390552, 17]-code) | [i] | ||
| 35 | Linear OA(586, 390654, F5, 13) (dual of [390654, 390568, 14]-code) | [i] | ||
| 36 | Linear OA(578, 390654, F5, 12) (dual of [390654, 390576, 13]-code) | [i] | ||
| 37 | Linear OA(570, 390654, F5, 11) (dual of [390654, 390584, 12]-code) | [i] | ||
| 38 | Linear OA(554, 390654, F5, 8) (dual of [390654, 390600, 9]-code) | [i] | ||
| 39 | Linear OA(5134, 390662, F5, 20) (dual of [390662, 390528, 21]-code) | [i] | ||
| 40 | Linear OA(570, 390662, F5, 10) (dual of [390662, 390592, 11]-code) | [i] | ||
| 41 | Linear OA(5118, 78158, F5, 20) (dual of [78158, 78040, 21]-code) | [i] | ||
| 42 | Linear OA(562, 78158, F5, 10) (dual of [78158, 78096, 11]-code) | [i] | ||
| 43 | Linear OA(5150, 15654, F5, 30) (dual of [15654, 15504, 31]-code) | [i] | ||
| 44 | Linear OA(5102, 15654, F5, 20) (dual of [15654, 15552, 21]-code) | [i] | ||
| 45 | Linear OA(554, 15654, F5, 10) (dual of [15654, 15600, 11]-code) | [i] | ||
| 46 | Linear OA(5144, 390658, F5, 22) (dual of [390658, 390514, 23]-code) | [i] | Construction XX with a Chain of Extended Narrow-Sense BCH Codes | |
| 47 | Linear OA(5143, 390656, F5, 22) (dual of [390656, 390513, 23]-code) | [i] | ||
| 48 | Linear OA(5136, 390658, F5, 21) (dual of [390658, 390522, 22]-code) | [i] | ||
| 49 | Linear OA(5135, 390656, F5, 21) (dual of [390656, 390521, 22]-code) | [i] | ||
| 50 | Linear OA(5120, 390658, F5, 18) (dual of [390658, 390538, 19]-code) | [i] | ||
| 51 | Linear OA(5119, 390656, F5, 18) (dual of [390656, 390537, 19]-code) | [i] | ||
| 52 | Linear OA(5112, 390658, F5, 17) (dual of [390658, 390546, 18]-code) | [i] | ||
| 53 | Linear OA(5111, 390656, F5, 17) (dual of [390656, 390545, 18]-code) | [i] | ||
| 54 | Linear OA(5104, 390658, F5, 16) (dual of [390658, 390554, 17]-code) | [i] | ||
| 55 | Linear OA(5103, 390656, F5, 16) (dual of [390656, 390553, 17]-code) | [i] | ||
| 56 | Linear OA(588, 390658, F5, 13) (dual of [390658, 390570, 14]-code) | [i] | ||
| 57 | Linear OA(587, 390656, F5, 13) (dual of [390656, 390569, 14]-code) | [i] | ||
| 58 | Linear OA(580, 390658, F5, 12) (dual of [390658, 390578, 13]-code) | [i] | ||
| 59 | Linear OA(579, 390656, F5, 12) (dual of [390656, 390577, 13]-code) | [i] | ||
| 60 | Linear OA(572, 390658, F5, 11) (dual of [390658, 390586, 12]-code) | [i] | ||
| 61 | Linear OA(571, 390656, F5, 11) (dual of [390656, 390585, 12]-code) | [i] | ||
| 62 | Linear OA(5148, 78155, F5, 26) (dual of [78155, 78007, 27]-code) | [i] | ||
| 63 | Linear OA(5134, 78155, F5, 23) (dual of [78155, 78021, 24]-code) | [i] | ||
| 64 | Linear OA(5127, 78155, F5, 22) (dual of [78155, 78028, 23]-code) | [i] | ||
| 65 | Linear OA(5120, 78155, F5, 21) (dual of [78155, 78035, 22]-code) | [i] | ||
| 66 | Linear OA(5106, 78155, F5, 18) (dual of [78155, 78049, 19]-code) | [i] | ||
| 67 | Linear OA(599, 78155, F5, 17) (dual of [78155, 78056, 18]-code) | [i] | ||
| 68 | Linear OA(592, 78155, F5, 16) (dual of [78155, 78063, 17]-code) | [i] | ||
| 69 | Linear OA(578, 78155, F5, 13) (dual of [78155, 78077, 14]-code) | [i] | ||
| 70 | Linear OA(571, 78155, F5, 12) (dual of [78155, 78084, 13]-code) | [i] | ||
| 71 | Linear OA(564, 78155, F5, 11) (dual of [78155, 78091, 12]-code) | [i] | ||
| 72 | Linear OA(5129, 15659, F5, 25) (dual of [15659, 15530, 26]-code) | [i] | ||
| 73 | Linear OA(5105, 15659, F5, 20) (dual of [15659, 15554, 21]-code) | [i] | ||
| 74 | Linear OA(5104, 15657, F5, 20) (dual of [15657, 15553, 21]-code) | [i] | ||
| 75 | Linear OA(581, 15659, F5, 15) (dual of [15659, 15578, 16]-code) | [i] | ||
| 76 | Linear OA(5150, 3157, F5, 35) (dual of [3157, 3007, 36]-code) | [i] | ||
| 77 | Linear OA(5130, 3157, F5, 30) (dual of [3157, 3027, 31]-code) | [i] | ||
| 78 | Linear OA(5110, 3157, F5, 25) (dual of [3157, 3047, 26]-code) | [i] | ||
| 79 | Linear OA(590, 3157, F5, 20) (dual of [3157, 3067, 21]-code) | [i] | ||
| 80 | Linear OA(570, 3157, F5, 15) (dual of [3157, 3087, 16]-code) | [i] | ||