Information on Result #1053797
Linear OOA(2237, 4109, F2, 4, 32) (dual of [(4109, 4), 16199, 33]-NRT-code), using OOA 4-folding based on linear OA(2237, 16436, F2, 32) (dual of [16436, 16199, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(2237, 16438, F2, 32) (dual of [16438, 16201, 33]-code), using
- 1 times truncation [i] based on linear OA(2238, 16439, F2, 33) (dual of [16439, 16201, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(26) [i] based on
- linear OA(2225, 16384, F2, 33) (dual of [16384, 16159, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(2183, 16384, F2, 27) (dual of [16384, 16201, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(213, 55, F2, 5) (dual of [55, 42, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(213, 63, F2, 5) (dual of [63, 50, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(213, 63, F2, 5) (dual of [63, 50, 6]-code), using
- construction X applied to Ce(32) ⊂ Ce(26) [i] based on
- 1 times truncation [i] based on linear OA(2238, 16439, F2, 33) (dual of [16439, 16201, 34]-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(2237, 4109, F2, 5, 32) (dual of [(4109, 5), 20308, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2237, 4109, F2, 6, 32) (dual of [(4109, 6), 24417, 33]-NRT-code) | [i] | ||
| 3 | Linear OOA(2237, 4109, F2, 7, 32) (dual of [(4109, 7), 28526, 33]-NRT-code) | [i] | ||
| 4 | Linear OOA(2237, 4109, F2, 8, 32) (dual of [(4109, 8), 32635, 33]-NRT-code) | [i] | ||
| 5 | Digital (205, 237, 4109)-net over F2 | [i] | ||