Information on Result #1297312
Linear OA(2166, 298, F2, 44) (dual of [298, 132, 45]-code), using construction X with Varšamov bound based on
- linear OA(2161, 292, F2, 44) (dual of [292, 131, 45]-code), using
- construction XX applied to C1 = C([213,254]), C2 = C([219,2]), C3 = C1 + C2 = C([219,254]), and C∩ = C1 ∩ C2 = C([213,2]) [i] based on
- linear OA(2140, 255, F2, 42) (dual of [255, 115, 43]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−42,−41,…,−1}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(2133, 255, F2, 39) (dual of [255, 122, 40]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−36,−35,…,2}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(2149, 255, F2, 45) (dual of [255, 106, 46]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−42,−41,…,2}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(2124, 255, F2, 36) (dual of [255, 131, 37]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−36,−35,…,−1}, and designed minimum distance d ≥ |I|+1 = 37 [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
- construction XX applied to C1 = C([213,254]), C2 = C([219,2]), C3 = C1 + C2 = C([219,254]), and C∩ = C1 ∩ C2 = C([213,2]) [i] based on
- linear OA(2161, 293, F2, 39) (dual of [293, 132, 40]-code), using Gilbert–Varšamov bound and bm = 2161 > Vbs−1(k−1) = 875505 189076 586178 542482 087534 910614 182952 910400 [i]
- linear OA(24, 5, F2, 4) (dual of [5, 1, 5]-code or 5-arc in PG(3,2)), using
- dual of repetition code with length 5 [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(2167, 299, F2, 45) (dual of [299, 132, 46]-code) | [i] | Adding a Parity Check Bit | |