Information on Result #809255
Linear OOA(2207, 273, F2, 2, 47) (dual of [(273, 2), 339, 48]-NRT-code), using OOA 2-folding based on linear OA(2207, 546, F2, 47) (dual of [546, 339, 48]-code), using
- discarding factors / shortening the dual code based on linear OA(2207, 547, F2, 47) (dual of [547, 340, 48]-code), using
- adding a parity check bit [i] based on linear OA(2206, 546, F2, 46) (dual of [546, 340, 47]-code), using
- construction XX applied to C1 = C([507,40]), C2 = C([1,42]), C3 = C1 + C2 = C([1,40]), and C∩ = C1 ∩ C2 = C([507,42]) [i] based on
- linear OA(2190, 511, F2, 45) (dual of [511, 321, 46]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,40}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(2180, 511, F2, 42) (dual of [511, 331, 43]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(2199, 511, F2, 47) (dual of [511, 312, 48]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,42}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(2171, 511, F2, 40) (dual of [511, 340, 41]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(26, 25, F2, 3) (dual of [25, 19, 4]-code or 25-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, 10, F2, 1) (dual of [10, 9, 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([507,40]), C2 = C([1,42]), C3 = C1 + C2 = C([1,40]), and C∩ = C1 ∩ C2 = C([507,42]) [i] based on
- adding a parity check bit [i] based on linear OA(2206, 546, F2, 46) (dual of [546, 340, 47]-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(2207, 273, F2, 2, 46) (dual of [(273, 2), 339, 47]-NRT-code) | [i] | Strength Reduction for OOAs | |