Information on Result #1096964
Linear OOA(2253, 13119, F2, 5, 30) (dual of [(13119, 5), 65342, 31]-NRT-code), using OOA 5-folding based on linear OA(2253, 65595, F2, 30) (dual of [65595, 65342, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(2253, 65596, F2, 30) (dual of [65596, 65343, 31]-code), using
- 1 times truncation [i] based on linear OA(2254, 65597, F2, 31) (dual of [65597, 65343, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(24) [i] based on
- linear OA(2241, 65536, F2, 31) (dual of [65536, 65295, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2193, 65536, F2, 25) (dual of [65536, 65343, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(213, 61, F2, 5) (dual of [61, 48, 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(30) ⊂ Ce(24) [i] based on
- 1 times truncation [i] based on linear OA(2254, 65597, F2, 31) (dual of [65597, 65343, 32]-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(2253, 12613, F2, 6, 30) (dual of [(12613, 6), 75425, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2253, 12613, F2, 7, 30) (dual of [(12613, 7), 88038, 31]-NRT-code) | [i] | ||
| 3 | Linear OOA(2253, 12613, F2, 8, 30) (dual of [(12613, 8), 100651, 31]-NRT-code) | [i] | ||
| 4 | Digital (223, 253, 12613)-net over F2 | [i] | ||