Information on Result #1151915
Linear OOA(2237, 74905, F2, 7, 25) (dual of [(74905, 7), 524098, 26]-NRT-code), using OOA 7-folding based on linear OA(2237, 524335, F2, 25) (dual of [524335, 524098, 26]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2236, 524334, F2, 25) (dual of [524334, 524098, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- linear OA(2229, 524289, F2, 25) (dual of [524289, 524060, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 524289 | 238−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(2191, 524289, F2, 21) (dual of [524289, 524098, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 524289 | 238−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(27, 45, F2, 3) (dual of [45, 38, 4]-code or 45-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
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(2238, 74905, F2, 7, 25) (dual of [(74905, 7), 524097, 26]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2239, 74905, F2, 7, 25) (dual of [(74905, 7), 524096, 26]-NRT-code) | [i] | ||
| 3 | Linear OOA(2240, 74905, F2, 7, 25) (dual of [(74905, 7), 524095, 26]-NRT-code) | [i] | ||
| 4 | Linear OOA(2237, 74905, F2, 8, 25) (dual of [(74905, 8), 599003, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Digital (212, 237, 74905)-net over F2 | [i] | ||