Information on Result #2175211
Linear OA(2239, 552, F2, 55) (dual of [552, 313, 56]-code), using adding a parity check bit based on linear OA(2238, 551, F2, 54) (dual of [551, 313, 55]-code), using
- construction XX applied to C1 = C([459,510]), C2 = C([465,2]), C3 = C1 + C2 = C([465,510]), and C∩ = C1 ∩ C2 = C([459,2]) [i] based on
- linear OA(2216, 511, F2, 52) (dual of [511, 295, 53]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−52,−51,…,−1}, and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(2208, 511, F2, 49) (dual of [511, 303, 50]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−46,−45,…,2}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(2226, 511, F2, 55) (dual of [511, 285, 56]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−52,−51,…,2}, and designed minimum distance d ≥ |I|+1 = 56 [i]
- linear OA(2198, 511, F2, 46) (dual of [511, 313, 47]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−46,−45,…,−1}, and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(211, 29, F2, 5) (dual of [29, 18, 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, 11, F2, 1) (dual of [11, 10, 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(2239, 552, F2, 54) (dual of [552, 313, 55]-code) | [i] | Strength Reduction | |
| 2 | Linear OOA(2239, 276, F2, 2, 55) (dual of [(276, 2), 313, 56]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2239, 184, F2, 3, 55) (dual of [(184, 3), 313, 56]-NRT-code) | [i] | ||
| 4 | Linear OOA(2239, 138, F2, 4, 55) (dual of [(138, 4), 313, 56]-NRT-code) | [i] | ||