Information on Result #1304032
Linear OA(2250, 580, F2, 54) (dual of [580, 330, 55]-code), using 9 step Varšamov–Edel lengthening with (ri) = (3, 1, 1, 1, 1, 0, 1, 0, 0) based on linear OA(2242, 563, F2, 54) (dual of [563, 321, 55]-code), using
- 1 times truncation [i] based on linear OA(2243, 564, F2, 55) (dual of [564, 321, 56]-code), using
- construction XX applied to C1 = C([461,0]), C2 = C([467,4]), C3 = C1 + C2 = C([467,0]), and C∩ = C1 ∩ C2 = C([461,4]) [i] based on
- linear OA(2208, 511, F2, 51) (dual of [511, 303, 52]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−50,−49,…,0}, and designed minimum distance d ≥ |I|+1 = 52 [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 = {−44,−43,…,4}, 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 = {−50,−49,…,4}, and designed minimum distance d ≥ |I|+1 = 56 [i]
- linear OA(2190, 511, F2, 45) (dual of [511, 321, 46]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−44,−43,…,0}, and designed minimum distance d ≥ |I|+1 = 46 [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(26, 24, F2, 3) (dual of [24, 18, 4]-code or 24-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction XX applied to C1 = C([461,0]), C2 = C([467,4]), C3 = C1 + C2 = C([467,0]), and C∩ = C1 ∩ C2 = C([461,4]) [i] based on
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(2251, 581, F2, 55) (dual of [581, 330, 56]-code) | [i] | Adding a Parity Check Bit | |