Information on Result #1708533
Linear OOA(283, 2736, F2, 18, 12) (dual of [(2736, 18), 49165, 13]-NRT-code), using OOA stacking with additional row based on linear OOA(283, 2737, F2, 6, 12) (dual of [(2737, 6), 16339, 13]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] 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
- OOA 3-folding [i] based on linear OA(283, 8211, F2, 12) (dual of [8211, 8128, 13]-code), using
Mode: Linear.
Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (71, 83, 2736)-net over F2 | [i] | Net Defined by OOA | |