Information on Result #1588698
Linear OOA(234, 113, F2, 4, 9) (dual of [(113, 4), 418, 10]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(234, 113, F2, 2, 9) (dual of [(113, 2), 192, 10]-NRT-code), using
- discarding factors / shortening the dual code 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
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n 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, 2097263, F2, 4, 18) (dual of [(2097263, 4), 8388811, 19]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2242, 2097263, F2, 4, 19) (dual of [(2097263, 4), 8388810, 20]-NRT-code) | [i] | ||
| 3 | Linear OOA(234, 112, F2, 5, 9) (dual of [(112, 5), 526, 10]-NRT-code) | [i] | OOA Stacking with Additional Row | |
| 4 | Linear OOA(234, 112, F2, 6, 9) (dual of [(112, 6), 638, 10]-NRT-code) | [i] | ||
| 5 | Linear OOA(234, 112, F2, 7, 9) (dual of [(112, 7), 750, 10]-NRT-code) | [i] | ||
| 6 | Linear OOA(234, 112, F2, 8, 9) (dual of [(112, 8), 862, 10]-NRT-code) | [i] | ||