Information on Result #1051396
Linear OOA(2103, 32772, F2, 4, 12) (dual of [(32772, 4), 130985, 13]-NRT-code), using OOA 4-folding based on linear OA(2103, 131088, F2, 12) (dual of [131088, 130985, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2103, 131090, F2, 12) (dual of [131090, 130987, 13]-code), using
- 1 times truncation [i] based on linear OA(2104, 131091, F2, 13) (dual of [131091, 130987, 14]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(2103, 131072, F2, 13) (dual of [131072, 130969, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(286, 131072, F2, 11) (dual of [131072, 130986, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(218, 19, F2, 17) (dual of [19, 1, 18]-code), using
- strength reduction [i] based on linear OA(218, 19, F2, 18) (dual of [19, 1, 19]-code or 19-arc in PG(17,2)), using
- dual of repetition code with length 19 [i]
- strength reduction [i] based on linear OA(218, 19, F2, 18) (dual of [19, 1, 19]-code or 19-arc in PG(17,2)), using
- linear OA(21, 19, F2, 1) (dual of [19, 18, 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(2104, 131091, F2, 13) (dual of [131091, 130987, 14]-code), using
Mode: Constructive and 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(2103, 32772, F2, 5, 12) (dual of [(32772, 5), 163757, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2103, 32772, F2, 6, 12) (dual of [(32772, 6), 196529, 13]-NRT-code) | [i] | ||
| 3 | Linear OOA(2103, 32772, F2, 7, 12) (dual of [(32772, 7), 229301, 13]-NRT-code) | [i] | ||
| 4 | Linear OOA(2103, 32772, F2, 8, 12) (dual of [(32772, 8), 262073, 13]-NRT-code) | [i] | ||
| 5 | Digital (91, 103, 32772)-net over F2 | [i] | ||