Information on Result #1116063
Linear OOA(2258, 1678747, F2, 5, 19) (dual of [(1678747, 5), 8393477, 20]-NRT-code), using (u, u+v)-construction based on
- linear OOA(250, 1027, F2, 5, 9) (dual of [(1027, 5), 5085, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(250, 4109, F2, 9) (dual of [4109, 4059, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(249, 4096, F2, 9) (dual of [4096, 4047, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(237, 4096, F2, 7) (dual of [4096, 4059, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(21, 13, F2, 1) (dual of [13, 12, 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 4-folding and stacking with additional row [i] based on linear OA(250, 4109, F2, 9) (dual of [4109, 4059, 10]-code), using
- linear OOA(2208, 1677720, F2, 5, 19) (dual of [(1677720, 5), 8388392, 20]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2208, 8388600, F2, 19) (dual of [8388600, 8388392, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- OOA 5-folding [i] based on linear OA(2208, 8388600, F2, 19) (dual of [8388600, 8388392, 20]-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(2258, 1678747, F2, 5, 18) (dual of [(1678747, 5), 8393477, 19]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2259, 1678747, F2, 5, 19) (dual of [(1678747, 5), 8393476, 20]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2260, 1678747, F2, 5, 19) (dual of [(1678747, 5), 8393475, 20]-NRT-code) | [i] | ||