Information on Result #1053324
Linear OOA(2183, 2051, F2, 4, 28) (dual of [(2051, 4), 8021, 29]-NRT-code), using OOA 4-folding based on linear OA(2183, 8204, F2, 28) (dual of [8204, 8021, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(2183, 8205, F2, 28) (dual of [8205, 8022, 29]-code), using
- 1 times truncation [i] based on linear OA(2184, 8206, F2, 29) (dual of [8206, 8022, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(26) [i] based on
- linear OA(2183, 8192, F2, 29) (dual of [8192, 8009, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2170, 8192, F2, 27) (dual of [8192, 8022, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(21, 14, F2, 1) (dual of [14, 13, 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(28) ⊂ Ce(26) [i] based on
- 1 times truncation [i] based on linear OA(2184, 8206, F2, 29) (dual of [8206, 8022, 30]-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(2183, 2043, F2, 5, 28) (dual of [(2043, 5), 10032, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
2 | Linear OOA(2183, 2043, F2, 6, 28) (dual of [(2043, 6), 12075, 29]-NRT-code) | [i] | ||
3 | Linear OOA(2183, 2043, F2, 7, 28) (dual of [(2043, 7), 14118, 29]-NRT-code) | [i] | ||
4 | Linear OOA(2183, 2043, F2, 8, 28) (dual of [(2043, 8), 16161, 29]-NRT-code) | [i] | ||
5 | Digital (155, 183, 2043)-net over F2 | [i] |