Information on Result #2668415
Linear OOA(2223, 2748, F2, 3, 32) (dual of [(2748, 3), 8021, 33]-NRT-code), using 21 times duplication based on linear OOA(2222, 2748, F2, 3, 32) (dual of [(2748, 3), 8022, 33]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2222, 8244, F2, 32) (dual of [8244, 8022, 33]-code), using
- strength reduction [i] based on linear OA(2222, 8244, F2, 33) (dual of [8244, 8022, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(26) [i] based on
- linear OA(2209, 8192, F2, 33) (dual of [8192, 7983, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [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(213, 52, F2, 5) (dual of [52, 39, 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
- strength reduction [i] based on linear OA(2222, 8244, F2, 33) (dual of [8244, 8022, 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(2223, 2579, F2, 4, 32) (dual of [(2579, 4), 10093, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2223, 2579, F2, 5, 32) (dual of [(2579, 5), 12672, 33]-NRT-code) | [i] | ||
| 3 | Linear OOA(2223, 2579, F2, 6, 32) (dual of [(2579, 6), 15251, 33]-NRT-code) | [i] | ||
| 4 | Linear OOA(2223, 2579, F2, 7, 32) (dual of [(2579, 7), 17830, 33]-NRT-code) | [i] | ||
| 5 | Linear OOA(2223, 2579, F2, 8, 32) (dual of [(2579, 8), 20409, 33]-NRT-code) | [i] | ||
| 6 | Digital (191, 223, 2579)-net over F2 | [i] | ||