Information on Result #1514715
Linear OOA(2192, 527, F2, 3, 38) (dual of [(527, 3), 1389, 39]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2192, 527, F2, 2, 38) (dual of [(527, 2), 862, 39]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2192, 1054, F2, 38) (dual of [1054, 862, 39]-code), using
- 1 times truncation [i] based on linear OA(2193, 1055, F2, 39) (dual of [1055, 862, 40]-code), using
- construction XX applied to C1 = C([1019,32]), C2 = C([0,34]), C3 = C1 + C2 = C([0,32]), and C∩ = C1 ∩ C2 = C([1019,34]) [i] based on
- linear OA(2181, 1023, F2, 37) (dual of [1023, 842, 38]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,32}, and designed minimum distance d ≥ |I|+1 = 38 [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(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(2161, 1023, F2, 33) (dual of [1023, 862, 34]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,32], and designed minimum distance d ≥ |I|+1 = 34 [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, 6, F2, 1) (dual of [6, 5, 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([1019,32]), C2 = C([0,34]), C3 = C1 + C2 = C([0,32]), and C∩ = C1 ∩ C2 = C([1019,34]) [i] based on
- 1 times truncation [i] based on linear OA(2193, 1055, F2, 39) (dual of [1055, 862, 40]-code), using
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(2192, 263, F2, 6, 38) (dual of [(263, 6), 1386, 39]-NRT-code) | [i] | OOA Folding | |