Information on Result #1297635
Linear OA(2258, 307, F2, 92) (dual of [307, 49, 93]-code), using construction X with Varšamov bound based on
- linear OA(2237, 284, F2, 92) (dual of [284, 47, 93]-code), using
- construction XX applied to C1 = C([165,254]), C2 = C([171,4]), C3 = C1 + C2 = C([171,254]), and C∩ = C1 ∩ C2 = C([165,4]) [i] based on
- linear OA(2218, 255, F2, 90) (dual of [255, 37, 91]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−90,−89,…,−1}, and designed minimum distance d ≥ |I|+1 = 91 [i]
- linear OA(2217, 255, F2, 89) (dual of [255, 38, 90]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−84,−83,…,4}, and designed minimum distance d ≥ |I|+1 = 90 [i]
- linear OA(2227, 255, F2, 95) (dual of [255, 28, 96]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−90,−89,…,4}, and designed minimum distance d ≥ |I|+1 = 96 [i]
- linear OA(2208, 255, F2, 84) (dual of [255, 47, 85]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−84,−83,…,−1}, and designed minimum distance d ≥ |I|+1 = 85 [i]
- linear OA(25, 15, F2, 3) (dual of [15, 10, 4]-code or 15-cap in PG(4,2)), using
- discarding factors / shortening the dual code based on linear OA(25, 16, F2, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,2)), using
- linear OA(25, 14, F2, 3) (dual of [14, 9, 4]-code or 14-cap in PG(4,2)), using
- discarding factors / shortening the dual code based on linear OA(25, 16, F2, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,2)) (see above)
- construction XX applied to C1 = C([165,254]), C2 = C([171,4]), C3 = C1 + C2 = C([171,254]), and C∩ = C1 ∩ C2 = C([165,4]) [i] based on
- linear OA(2237, 286, F2, 78) (dual of [286, 49, 79]-code), using Gilbert–Varšamov bound and bm = 2237 > Vbs−1(k−1) = 136906 111056 314432 414314 111958 692500 589416 844771 284194 963917 078665 182368 [i]
- linear OA(219, 21, F2, 13) (dual of [21, 2, 14]-code), using
- repeating each code word 7 times [i] based on linear OA(21, 3, F2, 1) (dual of [3, 2, 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
- repeating each code word 7 times [i] based on linear OA(21, 3, F2, 1) (dual of [3, 2, 2]-code), using
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(2260, 309, F2, 92) (dual of [309, 49, 93]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(2259, 308, F2, 93) (dual of [308, 49, 94]-code) | [i] | Adding a Parity Check Bit | |