Information on Result #1175814
Linear OOA(2222, 1048705, F2, 8, 17) (dual of [(1048705, 8), 8389418, 18]-NRT-code), using (u, u+v)-construction based on
- linear OOA(237, 130, F2, 8, 8) (dual of [(130, 8), 1003, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(237, 520, F2, 8) (dual of [520, 483, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(237, 522, F2, 8) (dual of [522, 485, 9]-code), using
- 1 times truncation [i] based on linear OA(238, 523, F2, 9) (dual of [523, 485, 10]-code), using
- construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(237, 512, F2, 9) (dual of [512, 475, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(228, 512, F2, 7) (dual of [512, 484, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(210, 11, F2, 9) (dual of [11, 1, 10]-code), using
- strength reduction [i] based on linear OA(210, 11, F2, 10) (dual of [11, 1, 11]-code or 11-arc in PG(9,2)), using
- dual of repetition code with length 11 [i]
- strength reduction [i] based on linear OA(210, 11, F2, 10) (dual of [11, 1, 11]-code or 11-arc in PG(9,2)), using
- linear OA(21, 11, F2, 1) (dual of [11, 10, 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
- 1 times truncation [i] based on linear OA(238, 523, F2, 9) (dual of [523, 485, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(237, 522, F2, 8) (dual of [522, 485, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(237, 520, F2, 8) (dual of [520, 483, 9]-code), using
- linear OOA(2185, 1048575, F2, 8, 17) (dual of [(1048575, 8), 8388415, 18]-NRT-code), using
- OOA 8-folding [i] based on linear OA(2185, 8388600, F2, 17) (dual of [8388600, 8388415, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- OOA 8-folding [i] based on linear OA(2185, 8388600, F2, 17) (dual of [8388600, 8388415, 18]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(2222, 1048704, F2, 24, 17) (dual of [(1048704, 24), 25168674, 18]-NRT-code) | [i] | OOA Stacking with Additional Row | |