Information on Result #674206
Linear OA(212, 38, F2, 5) (dual of [38, 26, 6]-code), using construction X applied to Ce(4) ⊂ Ce(2) based on
- linear OA(211, 32, F2, 5) (dual of [32, 21, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(21, 6, F2, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
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(2104, 291, F2, 24) (dual of [291, 187, 25]-code) | [i] | Construction X with Cyclic Codes | |
| 2 | Linear OA(2112, 291, F2, 26) (dual of [291, 179, 27]-code) | [i] | ||
| 3 | Linear OA(2120, 291, F2, 28) (dual of [291, 171, 29]-code) | [i] | ||
| 4 | Linear OA(2128, 291, F2, 30) (dual of [291, 163, 31]-code) | [i] | ||
| 5 | Linear OA(2137, 291, F2, 33) (dual of [291, 154, 34]-code) | [i] | ||
| 6 | Linear OA(2136, 291, F2, 32) (dual of [291, 155, 33]-code) | [i] | ||
| 7 | Linear OA(2177, 291, F2, 49) (dual of [291, 114, 50]-code) | [i] | ||
| 8 | Linear OA(2176, 291, F2, 48) (dual of [291, 115, 49]-code) | [i] | ||
| 9 | Linear OA(2177, 1060, F2, 34) (dual of [1060, 883, 35]-code) | [i] | ||
| 10 | Linear OA(2187, 1060, F2, 36) (dual of [1060, 873, 37]-code) | [i] | ||
| 11 | Linear OA(2106, 296, F2, 24) (dual of [296, 190, 25]-code) | [i] | Construction XX with Cyclic Codes | |
| 12 | Linear OA(2106, 296, F2, 25) (dual of [296, 190, 26]-code) | [i] | ||
| 13 | Linear OA(2114, 300, F2, 26) (dual of [300, 186, 27]-code) | [i] | ||
| 14 | Linear OA(2114, 300, F2, 27) (dual of [300, 186, 28]-code) | [i] | ||
| 15 | Linear OA(2117, 304, F2, 27) (dual of [304, 187, 28]-code) | [i] | ||
| 16 | Linear OA(2114, 301, F2, 26) (dual of [301, 187, 27]-code) | [i] | ||
| 17 | Linear OA(2122, 300, F2, 28) (dual of [300, 178, 29]-code) | [i] | ||
| 18 | Linear OA(2122, 300, F2, 29) (dual of [300, 178, 30]-code) | [i] | ||
| 19 | Linear OA(2125, 304, F2, 29) (dual of [304, 179, 30]-code) | [i] | ||
| 20 | Linear OA(2122, 301, F2, 28) (dual of [301, 179, 29]-code) | [i] | ||
| 21 | Linear OA(2130, 300, F2, 30) (dual of [300, 170, 31]-code) | [i] | ||
| 22 | Linear OA(2130, 300, F2, 31) (dual of [300, 170, 32]-code) | [i] | ||
| 23 | Linear OA(2133, 304, F2, 31) (dual of [304, 171, 32]-code) | [i] | ||
| 24 | Linear OA(2130, 301, F2, 30) (dual of [301, 171, 31]-code) | [i] | ||
| 25 | Linear OA(2138, 300, F2, 33) (dual of [300, 162, 34]-code) | [i] | ||
| 26 | Linear OA(2138, 301, F2, 32) (dual of [301, 163, 33]-code) | [i] | ||
| 27 | Linear OA(2149, 557, F2, 30) (dual of [557, 408, 31]-code) | [i] | ||
| 28 | Linear OA(2158, 557, F2, 32) (dual of [557, 399, 33]-code) | [i] | ||
| 29 | Linear OA(2189, 561, F2, 40) (dual of [561, 372, 41]-code) | [i] | ||
| 30 | Linear OA(2204, 576, F2, 42) (dual of [576, 372, 43]-code) | [i] | ||
| 31 | Linear OA(2194, 557, F2, 42) (dual of [557, 363, 43]-code) | [i] | ||
| 32 | Linear OA(2208, 571, F2, 44) (dual of [571, 363, 45]-code) | [i] | ||
| 33 | Linear OA(2203, 557, F2, 44) (dual of [557, 354, 45]-code) | [i] | ||
| 34 | Linear OA(2217, 571, F2, 46) (dual of [571, 354, 47]-code) | [i] | ||
| 35 | Linear OA(2212, 557, F2, 46) (dual of [557, 345, 47]-code) | [i] | ||
| 36 | Linear OA(2226, 571, F2, 48) (dual of [571, 345, 49]-code) | [i] | ||
| 37 | Linear OA(2221, 557, F2, 48) (dual of [557, 336, 49]-code) | [i] | ||
| 38 | Linear OA(2258, 576, F2, 56) (dual of [576, 318, 57]-code) | [i] | ||
| 39 | Linear OA(2252, 561, F2, 56) (dual of [561, 309, 57]-code) | [i] | ||
| 40 | Linear OA(2257, 557, F2, 58) (dual of [557, 300, 59]-code) | [i] | ||
| 41 | Linear OA(2164, 1070, F2, 30) (dual of [1070, 906, 31]-code) | [i] | ||
| 42 | Linear OA(2174, 1070, F2, 32) (dual of [1070, 896, 33]-code) | [i] | ||
| 43 | Linear OA(2189, 1071, F2, 36) (dual of [1071, 882, 37]-code) | [i] | ||
| 44 | Linear OA(2199, 1071, F2, 38) (dual of [1071, 872, 39]-code) | [i] | ||
| 45 | Linear OA(2204, 1086, F2, 38) (dual of [1086, 882, 39]-code) | [i] | ||
| 46 | Linear OA(2214, 1080, F2, 40) (dual of [1080, 866, 41]-code) | [i] | ||
| 47 | Linear OA(2219, 1095, F2, 40) (dual of [1095, 876, 41]-code) | [i] | ||
| 48 | Linear OA(2209, 1071, F2, 40) (dual of [1071, 862, 41]-code) | [i] | ||
| 49 | Linear OA(2214, 1086, F2, 40) (dual of [1086, 872, 41]-code) | [i] | ||
| 50 | Linear OA(2219, 1070, F2, 42) (dual of [1070, 851, 43]-code) | [i] | ||
| 51 | Linear OA(2229, 1095, F2, 42) (dual of [1095, 866, 43]-code) | [i] | ||
| 52 | Linear OA(2224, 1086, F2, 42) (dual of [1086, 862, 43]-code) | [i] | ||
| 53 | Linear OA(2234, 1085, F2, 44) (dual of [1085, 851, 45]-code) | [i] | ||
| 54 | Linear OA(2229, 1070, F2, 44) (dual of [1070, 841, 45]-code) | [i] | ||
| 55 | Linear OA(2239, 1095, F2, 44) (dual of [1095, 856, 45]-code) | [i] | ||
| 56 | Linear OA(2244, 1085, F2, 46) (dual of [1085, 841, 47]-code) | [i] | ||
| 57 | Linear OA(2239, 1070, F2, 46) (dual of [1070, 831, 47]-code) | [i] | ||
| 58 | Linear OA(2249, 1095, F2, 46) (dual of [1095, 846, 47]-code) | [i] | ||
| 59 | Linear OA(2254, 1085, F2, 48) (dual of [1085, 831, 49]-code) | [i] | ||
| 60 | Linear OA(2249, 1070, F2, 48) (dual of [1070, 821, 49]-code) | [i] | ||
| 61 | Linear OA(2259, 1095, F2, 48) (dual of [1095, 836, 49]-code) | [i] | ||
| 62 | Linear OA(2259, 1070, F2, 50) (dual of [1070, 811, 51]-code) | [i] | ||