Information on Result #1680167
Linear OOA(2109, 4194566, F2, 7, 8) (dual of [(4194566, 7), 29361853, 9]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2109, 4194566, F2, 2, 8) (dual of [(4194566, 2), 8389023, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(217, 265, F2, 2, 4) (dual of [(265, 2), 513, 5]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(217, 265, F2, 4) (dual of [265, 248, 5]-code), using
- 1 times truncation [i] based on linear OA(218, 266, F2, 5) (dual of [266, 248, 6]-code), using
- construction X4 applied to Ce(4) ⊂ Ce(2) [i] based on
- linear OA(217, 256, F2, 5) (dual of [256, 239, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(29, 256, F2, 3) (dual of [256, 247, 4]-code or 256-cap in PG(8,2)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [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(4) ⊂ Ce(2) [i] based on
- 1 times truncation [i] based on linear OA(218, 266, F2, 5) (dual of [266, 248, 6]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(217, 265, F2, 4) (dual of [265, 248, 5]-code), using
- linear OOA(292, 4194301, F2, 2, 8) (dual of [(4194301, 2), 8388510, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(292, 8388602, F2, 8) (dual of [8388602, 8388510, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(292, large, F2, 8) (dual of [large, large−92, 9]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(292, large, F2, 8) (dual of [large, large−92, 9]-code), using
- OOA 2-folding [i] based on linear OA(292, 8388602, F2, 8) (dual of [8388602, 8388510, 9]-code), using
- linear OOA(217, 265, F2, 2, 4) (dual of [(265, 2), 513, 5]-NRT-code), using
Mode: 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(2109, 4194566, F2, 8, 8) (dual of [(4194566, 8), 33556419, 9]-NRT-code) | [i] | Appending kth Column | |