Information on Result #1052177
Linear OOA(2241, 2097217, F2, 4, 18) (dual of [(2097217, 4), 8388627, 19]-NRT-code), using OOA 2-folding based on linear OOA(2241, 4194434, F2, 2, 18) (dual of [(4194434, 2), 8388627, 19]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(234, 133, F2, 2, 9) (dual of [(133, 2), 232, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(234, 266, F2, 9) (dual of [266, 232, 10]-code), using
- construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(233, 256, F2, 9) (dual of [256, 223, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(225, 256, F2, 7) (dual of [256, 231, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(29, 10, F2, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,2)), using
- dual of repetition code with length 10 [i]
- linear OA(21, 10, F2, 1) (dual of [10, 9, 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
- OOA 2-folding [i] based on linear OA(234, 266, F2, 9) (dual of [266, 232, 10]-code), using
- linear OOA(2207, 4194301, F2, 2, 18) (dual of [(4194301, 2), 8388395, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2207, 8388602, F2, 18) (dual of [8388602, 8388395, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2207, large, F2, 18) (dual of [large, large−207, 19]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(2207, large, F2, 18) (dual of [large, large−207, 19]-code), using
- OOA 2-folding [i] based on linear OA(2207, 8388602, F2, 18) (dual of [8388602, 8388395, 19]-code), using
- linear OOA(234, 133, F2, 2, 9) (dual of [(133, 2), 232, 10]-NRT-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(2241, 1743452, F2, 5, 18) (dual of [(1743452, 5), 8717019, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2241, 1743452, F2, 6, 18) (dual of [(1743452, 6), 10460471, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(2241, 1743452, F2, 7, 18) (dual of [(1743452, 7), 12203923, 19]-NRT-code) | [i] | ||
| 4 | Linear OOA(2241, 1743452, F2, 8, 18) (dual of [(1743452, 8), 13947375, 19]-NRT-code) | [i] | ||
| 5 | Digital (223, 241, 1743452)-net over F2 | [i] | ||