Information on Result #2175005
Linear OA(2131, 302, F2, 31) (dual of [302, 171, 32]-code), using adding a parity check bit based on linear OA(2130, 301, F2, 30) (dual of [301, 171, 31]-code), using
- construction XX applied to C1 = C([227,254]), C2 = C([233,2]), C3 = C1 + C2 = C([233,254]), and C∩ = C1 ∩ C2 = C([227,2]) [i] based on
- linear OA(2108, 255, F2, 28) (dual of [255, 147, 29]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−28,−27,…,−1}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(293, 255, F2, 25) (dual of [255, 162, 26]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−22,−21,…,2}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(2117, 255, F2, 31) (dual of [255, 138, 32]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−28,−27,…,2}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(284, 255, F2, 22) (dual of [255, 171, 23]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−22,−21,…,−1}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(212, 36, F2, 5) (dual of [36, 24, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(212, 38, F2, 5) (dual of [38, 26, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(2) [i] based on
- linear OA(211, 32, F2, 5) (dual of [32, 21, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- 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 X applied to Ce(4) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(212, 38, F2, 5) (dual of [38, 26, 6]-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 (see above)
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 OA(2131, 302, F2, 30) (dual of [302, 171, 31]-code) | [i] | Strength Reduction | |
| 2 | Linear OOA(2131, 151, F2, 2, 31) (dual of [(151, 2), 171, 32]-NRT-code) | [i] | OOA Folding | |