Information on Result #702244
Linear OA(2120, 550, F2, 25) (dual of [550, 430, 26]-code), using construction XX applied to C1 = C([507,18]), C2 = C([1,20]), C3 = C1 + C2 = C([1,18]), and C∩ = C1 ∩ C2 = C([507,20]) based on
- linear OA(2100, 511, F2, 23) (dual of [511, 411, 24]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,18}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(290, 511, F2, 20) (dual of [511, 421, 21]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2109, 511, F2, 25) (dual of [511, 402, 26]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,20}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(281, 511, F2, 18) (dual of [511, 430, 19]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(210, 29, F2, 4) (dual of [29, 19, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(210, 32, F2, 4) (dual of [32, 22, 5]-code), using
- 1 times truncation [i] based on linear OA(211, 33, F2, 5) (dual of [33, 22, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33 | 210−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(211, 33, F2, 5) (dual of [33, 22, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(210, 32, F2, 4) (dual of [32, 22, 5]-code), 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
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(2120, 110, F2, 5, 25) (dual of [(110, 5), 430, 26]-NRT-code) | [i] | OOA Folding | |