Information on Result #1662200
Linear OOA(283, 2737, F2, 6, 12) (dual of [(2737, 6), 16339, 13]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(283, 2737, F2, 3, 12) (dual of [(2737, 3), 8128, 13]-NRT-code), using
- OOA 3-folding [i] based on linear OA(283, 8211, F2, 12) (dual of [8211, 8128, 13]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(279, 8206, F2, 12) (dual of [8206, 8127, 13]-code), using
- 1 times truncation [i] based on linear OA(280, 8207, F2, 13) (dual of [8207, 8127, 14]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(279, 8192, F2, 13) (dual of [8192, 8113, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(266, 8192, F2, 11) (dual of [8192, 8126, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(214, 15, F2, 13) (dual of [15, 1, 14]-code), using
- strength reduction [i] based on linear OA(214, 15, F2, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,2)), using
- dual of repetition code with length 15 [i]
- strength reduction [i] based on linear OA(214, 15, F2, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,2)), using
- linear OA(21, 15, F2, 1) (dual of [15, 14, 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(12) ⊂ Ce(10) [i] based on
- 1 times truncation [i] based on linear OA(280, 8207, F2, 13) (dual of [8207, 8127, 14]-code), using
- linear OA(279, 8207, F2, 8) (dual of [8207, 8128, 9]-code), using Gilbert–Varšamov bound and bm = 279 > Vbs−1(k−1) = 496305 635124 147541 989044 [i]
- linear OA(23, 4, F2, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,2) or 4-cap in PG(2,2)), using
- dual of repetition code with length 4 [i]
- caps in base b = 2 [i]
- linear OA(279, 8206, F2, 12) (dual of [8206, 8127, 13]-code), using
- construction X with Varšamov bound [i] based on
Mode: 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(283, 2736, F2, 7, 12) (dual of [(2736, 7), 19069, 13]-NRT-code) | [i] | OOA Stacking with Additional Row | |
| 2 | Linear OOA(283, 2736, F2, 8, 12) (dual of [(2736, 8), 21805, 13]-NRT-code) | [i] | ||
| 3 | Linear OOA(283, 2736, F2, 18, 12) (dual of [(2736, 18), 49165, 13]-NRT-code) | [i] | ||