Information on Result #894442
Linear OOA(2237, 4194369, F2, 2, 18) (dual of [(4194369, 2), 8388501, 19]-NRT-code), using (u, u+v)-construction based on
- linear OOA(230, 68, F2, 2, 9) (dual of [(68, 2), 106, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(230, 136, F2, 9) (dual of [136, 106, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(229, 128, F2, 9) (dual of [128, 99, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(222, 128, F2, 7) (dual of [128, 106, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(21, 8, F2, 1) (dual of [8, 7, 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 X applied to Ce(8) ⊂ Ce(6) [i] based on
- OOA 2-folding [i] based on linear OA(230, 136, F2, 9) (dual of [136, 106, 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
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(2237, 2097184, F2, 4, 18) (dual of [(2097184, 4), 8388499, 19]-NRT-code) | [i] | OOA Folding | |