Information on Result #674209
Linear OA(212, 39, F2, 5) (dual of [39, 27, 6]-code), using construction X4 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(26, 7, F2, 5) (dual of [7, 1, 6]-code), using
- strength reduction [i] based on linear OA(26, 7, F2, 6) (dual of [7, 1, 7]-code or 7-arc in PG(5,2)), using
- dual of repetition code with length 7 [i]
- strength reduction [i] based on linear OA(26, 7, F2, 6) (dual of [7, 1, 7]-code or 7-arc in PG(5,2)), using
- linear OA(21, 7, F2, 1) (dual of [7, 6, 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(2129, 550, F2, 26) (dual of [550, 421, 27]-code) | [i] | Construction X with Cyclic Codes | |
| 2 | Linear OA(2138, 550, F2, 28) (dual of [550, 412, 29]-code) | [i] | ||
| 3 | Linear OA(2147, 550, F2, 30) (dual of [550, 403, 31]-code) | [i] | ||
| 4 | Linear OA(2157, 550, F2, 33) (dual of [550, 393, 34]-code) | [i] | ||
| 5 | Linear OA(2156, 550, F2, 32) (dual of [550, 394, 33]-code) | [i] | ||
| 6 | Linear OA(2183, 550, F2, 40) (dual of [550, 367, 41]-code) | [i] | ||
| 7 | Linear OA(2192, 550, F2, 42) (dual of [550, 358, 43]-code) | [i] | ||
| 8 | Linear OA(2201, 550, F2, 44) (dual of [550, 349, 45]-code) | [i] | ||
| 9 | Linear OA(2210, 550, F2, 46) (dual of [550, 340, 47]-code) | [i] | ||
| 10 | Linear OA(2220, 550, F2, 49) (dual of [550, 330, 50]-code) | [i] | ||
| 11 | Linear OA(2219, 550, F2, 48) (dual of [550, 331, 49]-code) | [i] | ||
| 12 | Linear OA(2246, 550, F2, 56) (dual of [550, 304, 57]-code) | [i] | ||
| 13 | Linear OA(2255, 550, F2, 58) (dual of [550, 295, 59]-code) | [i] | ||
| 14 | Linear OA(2142, 1062, F2, 26) (dual of [1062, 920, 27]-code) | [i] | ||
| 15 | Linear OA(2152, 1062, F2, 28) (dual of [1062, 910, 29]-code) | [i] | ||
| 16 | Linear OA(2162, 1062, F2, 30) (dual of [1062, 900, 31]-code) | [i] | ||
| 17 | Linear OA(2172, 1062, F2, 32) (dual of [1062, 890, 33]-code) | [i] | ||
| 18 | Linear OA(2207, 1062, F2, 40) (dual of [1062, 855, 41]-code) | [i] | ||
| 19 | Linear OA(2217, 1062, F2, 42) (dual of [1062, 845, 43]-code) | [i] | ||
| 20 | Linear OA(2227, 1062, F2, 44) (dual of [1062, 835, 45]-code) | [i] | ||
| 21 | Linear OA(2237, 1062, F2, 46) (dual of [1062, 825, 47]-code) | [i] | ||
| 22 | Linear OA(2247, 1062, F2, 48) (dual of [1062, 815, 49]-code) | [i] | ||
| 23 | Linear OA(2257, 1062, F2, 50) (dual of [1062, 805, 51]-code) | [i] | ||