Information on Result #674069
Linear OA(286, 145, F2, 27) (dual of [145, 59, 28]-code), using construction XX applied to Ce(26) ⊂ Ce(22) ⊂ Ce(20) based on
- linear OA(278, 128, F2, 27) (dual of [128, 50, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(271, 128, F2, 23) (dual of [128, 57, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(264, 128, F2, 21) (dual of [128, 64, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(25, 14, F2, 3) (dual of [14, 9, 4]-code or 14-cap in PG(4,2)), using
- discarding factors / shortening the dual code based on linear OA(25, 16, F2, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,2)), using
- linear OA(21, 3, F2, 1) (dual of [3, 2, 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(285, 144, F2, 26) (dual of [144, 59, 27]-code) | [i] | Truncation | |
| 2 | Linear OOA(286, 72, F2, 2, 27) (dual of [(72, 2), 58, 28]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(286, 48, F2, 3, 27) (dual of [(48, 3), 58, 28]-NRT-code) | [i] | ||