Information on Result #1297266
Linear OA(2139, 290, F2, 34) (dual of [290, 151, 35]-code), using construction X with Varšamov bound based on
- linear OA(2136, 286, F2, 34) (dual of [286, 150, 35]-code), using
- 1 times truncation [i] based on linear OA(2137, 287, F2, 35) (dual of [287, 150, 36]-code), using
- construction XX applied to C1 = C([239,16]), C2 = C([237,10]), C3 = C1 + C2 = C([239,10]), and C∩ = C1 ∩ C2 = C([237,16]) [i] based on
- linear OA(2121, 255, F2, 33) (dual of [255, 134, 34]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−16,−15,…,16}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(2109, 255, F2, 29) (dual of [255, 146, 30]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−18,−17,…,10}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(2125, 255, F2, 35) (dual of [255, 130, 36]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−18,−17,…,16}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(2105, 255, F2, 27) (dual of [255, 150, 28]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−16,−15,…,10}, and designed minimum distance d ≥ |I|+1 = 28 [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, 5, F2, 1) (dual of [5, 4, 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 XX applied to C1 = C([239,16]), C2 = C([237,10]), C3 = C1 + C2 = C([239,10]), and C∩ = C1 ∩ C2 = C([237,16]) [i] based on
- 1 times truncation [i] based on linear OA(2137, 287, F2, 35) (dual of [287, 150, 36]-code), using
- linear OA(2136, 287, F2, 31) (dual of [287, 151, 32]-code), using Gilbert–Varšamov bound and bm = 2136 > Vbs−1(k−1) = 43294 970389 218393 618802 153632 403768 940672 [i]
- linear OA(22, 3, F2, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,2)), using
- dual of repetition code with length 3 [i]
- Hamming code H(2,2) [i]
Mode: 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(2140, 291, F2, 35) (dual of [291, 151, 36]-code) | [i] | Adding a Parity Check Bit | |