Information on Result #673897
Linear OA(279, 281, F2, 19) (dual of [281, 202, 20]-code), using construction XX applied to Ce(18) ⊂ Ce(14) ⊂ Ce(12) based on
- linear OA(269, 256, F2, 19) (dual of [256, 187, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(257, 256, F2, 15) (dual of [256, 199, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(249, 256, F2, 13) (dual of [256, 207, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(26, 21, F2, 3) (dual of [21, 15, 4]-code or 21-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- linear OA(21, 4, F2, 1) (dual of [4, 3, 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(278, 280, F2, 18) (dual of [280, 202, 19]-code) | [i] | Truncation | |
| 2 | Linear OOA(279, 140, F2, 2, 19) (dual of [(140, 2), 201, 20]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(279, 70, F2, 4, 19) (dual of [(70, 4), 201, 20]-NRT-code) | [i] | ||
| 4 | Linear OOA(279, 56, F2, 5, 19) (dual of [(56, 5), 201, 20]-NRT-code) | [i] | ||