Information on Result #1616125
Linear OOA(2249, 2097495, F2, 4, 18) (dual of [(2097495, 4), 8389731, 19]-NRT-code), using (u, u+v)-construction based on
- linear OOA(242, 345, F2, 4, 9) (dual of [(345, 4), 1338, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(242, 345, F2, 3, 9) (dual of [(345, 3), 993, 10]-NRT-code), using
- OOA 3-folding [i] based on linear OA(242, 1035, F2, 9) (dual of [1035, 993, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(241, 1024, F2, 9) (dual of [1024, 983, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(231, 1024, F2, 7) (dual of [1024, 993, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- 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 X applied to Ce(8) ⊂ Ce(6) [i] based on
- OOA 3-folding [i] based on linear OA(242, 1035, F2, 9) (dual of [1035, 993, 10]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(242, 345, F2, 3, 9) (dual of [(345, 3), 993, 10]-NRT-code), using
- linear OOA(2207, 2097150, F2, 4, 18) (dual of [(2097150, 4), 8388393, 19]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2207, 8388600, F2, 18) (dual of [8388600, 8388393, 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 4-folding [i] based on linear OA(2207, 8388600, F2, 18) (dual of [8388600, 8388393, 19]-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(2249, 2097495, F2, 5, 18) (dual of [(2097495, 5), 10487226, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2249, 2097495, F2, 6, 18) (dual of [(2097495, 6), 12584721, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(2249, 2097495, F2, 7, 18) (dual of [(2097495, 7), 14682216, 19]-NRT-code) | [i] | ||
| 4 | Linear OOA(2249, 2097495, F2, 8, 18) (dual of [(2097495, 8), 16779711, 19]-NRT-code) | [i] | ||
| 5 | Digital (231, 249, 2097495)-net over F2 | [i] | ||