Information on Result #673898
Linear OA(278, 279, F2, 19) (dual of [279, 201, 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, 20, F2, 3) (dual of [20, 14, 4]-code or 20-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, 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(277, 278, F2, 18) (dual of [278, 201, 19]-code) | [i] | Truncation | |
| 2 | Linear OOA(278, 139, F2, 2, 19) (dual of [(139, 2), 200, 20]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(278, 93, F2, 3, 19) (dual of [(93, 3), 201, 20]-NRT-code) | [i] | ||