Information on Result #1303931
Linear OA(2222, 582, F2, 46) (dual of [582, 360, 47]-code), using 12 step Varšamov–Edel lengthening with (ri) = (4, 2, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0) based on linear OA(2210, 558, F2, 46) (dual of [558, 348, 47]-code), using
- 1 times truncation [i] based on linear OA(2211, 559, F2, 47) (dual of [559, 348, 48]-code), using
- construction XX applied to C1 = C([507,38]), C2 = C([0,42]), C3 = C1 + C2 = C([0,38]), and C∩ = C1 ∩ C2 = C([507,42]) [i] based on
- linear OA(2181, 511, F2, 43) (dual of [511, 330, 44]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,38}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(2181, 511, F2, 43) (dual of [511, 330, 44]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,42], and designed minimum distance d ≥ |I|+1 = 44 [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(2163, 511, F2, 39) (dual of [511, 348, 40]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,38], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(26, 24, F2, 3) (dual of [24, 18, 4]-code or 24-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(26, 24, F2, 3) (dual of [24, 18, 4]-code or 24-cap in PG(5,2)) (see above)
- construction XX applied to C1 = C([507,38]), C2 = C([0,42]), C3 = C1 + C2 = C([0,38]), and C∩ = C1 ∩ C2 = C([507,42]) [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 OA(2223, 583, F2, 47) (dual of [583, 360, 48]-code) | [i] | Adding a Parity Check Bit | |