Information on Result #2921505
Linear OOA(2213, 349529, F2, 6, 20) (dual of [(349529, 6), 2096961, 21]-NRT-code), using 22 times duplication based on linear OOA(2211, 349529, F2, 6, 20) (dual of [(349529, 6), 2096963, 21]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2211, 2097174, F2, 20) (dual of [2097174, 2096963, 21]-code), using
- 1 times truncation [i] based on linear OA(2212, 2097175, F2, 21) (dual of [2097175, 2096963, 22]-code), using
- construction X4 applied to Ce(20) ⊂ Ce(18) [i] based on
- linear OA(2211, 2097152, F2, 21) (dual of [2097152, 2096941, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2190, 2097152, F2, 19) (dual of [2097152, 2096962, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(222, 23, F2, 21) (dual of [23, 1, 22]-code), using
- strength reduction [i] based on linear OA(222, 23, F2, 22) (dual of [23, 1, 23]-code or 23-arc in PG(21,2)), using
- dual of repetition code with length 23 [i]
- strength reduction [i] based on linear OA(222, 23, F2, 22) (dual of [23, 1, 23]-code or 23-arc in PG(21,2)), using
- linear OA(21, 23, F2, 1) (dual of [23, 22, 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(20) ⊂ Ce(18) [i] based on
- 1 times truncation [i] based on linear OA(2212, 2097175, F2, 21) (dual of [2097175, 2096963, 22]-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(2213, 349529, F2, 7, 20) (dual of [(349529, 7), 2446490, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2213, 349529, F2, 8, 20) (dual of [(349529, 8), 2796019, 21]-NRT-code) | [i] | ||
| 3 | Digital (193, 213, 349529)-net over F2 | [i] | ||