Information on Result #2175094
Linear OA(2170, 293, F2, 47) (dual of [293, 123, 48]-code), using adding a parity check bit based on linear OA(2169, 292, F2, 46) (dual of [292, 123, 47]-code), using
- construction XX applied to C1 = C([211,254]), C2 = C([217,2]), C3 = C1 + C2 = C([217,254]), and C∩ = C1 ∩ C2 = C([211,2]) [i] based on
- linear OA(2148, 255, F2, 44) (dual of [255, 107, 45]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−44,−43,…,−1}, and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(2141, 255, F2, 41) (dual of [255, 114, 42]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−38,−37,…,2}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(2157, 255, F2, 47) (dual of [255, 98, 48]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−44,−43,…,2}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(2132, 255, F2, 38) (dual of [255, 123, 39]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−38,−37,…,−1}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(211, 27, F2, 5) (dual of [27, 16, 6]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(211, 32, F2, 5) (dual of [32, 21, 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, 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 OA(2170, 293, F2, 46) (dual of [293, 123, 47]-code) | [i] | Strength Reduction | |