Information on Result #945095
Linear OOA(268, 21852, F2, 3, 9) (dual of [(21852, 3), 65488, 10]-NRT-code), using OOA 3-folding based on linear OA(268, 65556, F2, 9) (dual of [65556, 65488, 10]-code), using
- 2 times code embedding in larger space [i] based on linear OA(266, 65554, F2, 9) (dual of [65554, 65488, 10]-code), using
- construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(265, 65536, F2, 9) (dual of [65536, 65471, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(249, 65536, F2, 7) (dual of [65536, 65487, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(217, 18, F2, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,2)), using
- dual of repetition code with length 18 [i]
- linear OA(21, 18, F2, 1) (dual of [18, 17, 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
- construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
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 OOA(267, 21851, F2, 3, 8) (dual of [(21851, 3), 65486, 9]-NRT-code) | [i] | Truncation for OOAs | |
| 2 | Linear OOA(268, 21335, F2, 4, 9) (dual of [(21335, 4), 85272, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(268, 21335, F2, 5, 9) (dual of [(21335, 5), 106607, 10]-NRT-code) | [i] | ||
| 4 | Linear OOA(268, 21335, F2, 6, 9) (dual of [(21335, 6), 127942, 10]-NRT-code) | [i] | ||
| 5 | Linear OOA(268, 21335, F2, 7, 9) (dual of [(21335, 7), 149277, 10]-NRT-code) | [i] | ||
| 6 | Linear OOA(268, 21335, F2, 8, 9) (dual of [(21335, 8), 170612, 10]-NRT-code) | [i] | ||