Information on Result #1515462
Linear OOA(2203, 530, F2, 3, 41) (dual of [(530, 3), 1387, 42]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2203, 530, F2, 2, 41) (dual of [(530, 2), 857, 42]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2203, 1060, F2, 41) (dual of [1060, 857, 42]-code), using
- construction XX applied to C1 = C([1019,34]), C2 = C([0,36]), C3 = C1 + C2 = C([0,34]), and C∩ = C1 ∩ C2 = C([1019,36]) [i] based on
- linear OA(2186, 1023, F2, 39) (dual of [1023, 837, 40]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,34}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(2176, 1023, F2, 37) (dual of [1023, 847, 38]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,36], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2196, 1023, F2, 41) (dual of [1023, 827, 42]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,36}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(2166, 1023, F2, 35) (dual of [1023, 857, 36]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,34], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(26, 26, F2, 3) (dual of [26, 20, 4]-code or 26-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- linear OA(21, 11, F2, 1) (dual of [11, 10, 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 XX applied to C1 = C([1019,34]), C2 = C([0,36]), C3 = C1 + C2 = C([0,34]), and C∩ = C1 ∩ C2 = C([1019,36]) [i] based on
Mode: 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(2203, 265, F2, 5, 41) (dual of [(265, 5), 1122, 42]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(2203, 265, F2, 6, 41) (dual of [(265, 6), 1387, 42]-NRT-code) | [i] | ||