Information on Result #702623
Linear OA(2251, 561, F2, 56) (dual of [561, 310, 57]-code), using construction XX applied to C1 = C([505,46]), C2 = C([0,50]), C3 = C1 + C2 = C([0,46]), and C∩ = C1 ∩ C2 = C([505,50]) based on
- linear OA(2226, 511, F2, 53) (dual of [511, 285, 54]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−6,−5,…,46}, and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(2208, 511, F2, 51) (dual of [511, 303, 52]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,50], and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(2235, 511, F2, 57) (dual of [511, 276, 58]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−6,−5,…,50}, and designed minimum distance d ≥ |I|+1 = 58 [i]
- linear OA(2199, 511, F2, 47) (dual of [511, 312, 48]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,46], and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(211, 36, F2, 4) (dual of [36, 25, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(211, 44, F2, 4) (dual of [44, 33, 5]-code), using
- linear OA(25, 14, F2, 3) (dual of [14, 9, 4]-code or 14-cap in PG(4,2)), using
- discarding factors / shortening the dual code based on linear OA(25, 16, F2, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,2)), 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(2251, 187, F2, 3, 56) (dual of [(187, 3), 310, 57]-NRT-code) | [i] | OOA Folding | |