Information on Result #1680396
Linear OOA(2115, 131077, F2, 7, 12) (dual of [(131077, 7), 917424, 13]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2115, 131077, F2, 4, 12) (dual of [(131077, 4), 524193, 13]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2115, 524308, F2, 12) (dual of [524308, 524193, 13]-code), using
- 1 times truncation [i] based on linear OA(2116, 524309, F2, 13) (dual of [524309, 524193, 14]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(2115, 524288, F2, 13) (dual of [524288, 524173, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(296, 524288, F2, 11) (dual of [524288, 524192, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(220, 21, F2, 19) (dual of [21, 1, 20]-code), using
- strength reduction [i] based on linear OA(220, 21, F2, 20) (dual of [21, 1, 21]-code or 21-arc in PG(19,2)), using
- dual of repetition code with length 21 [i]
- strength reduction [i] based on linear OA(220, 21, F2, 20) (dual of [21, 1, 21]-code or 21-arc in PG(19,2)), using
- linear OA(21, 21, F2, 1) (dual of [21, 20, 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(12) ⊂ Ce(10) [i] based on
- 1 times truncation [i] based on linear OA(2116, 524309, F2, 13) (dual of [524309, 524193, 14]-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(2116, 131077, F2, 7, 12) (dual of [(131077, 7), 917423, 13]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2117, 131077, F2, 7, 12) (dual of [(131077, 7), 917422, 13]-NRT-code) | [i] | ||
| 3 | Linear OOA(2118, 131077, F2, 7, 12) (dual of [(131077, 7), 917421, 13]-NRT-code) | [i] | ||