Information on Result #1303948
Linear OA(2234, 606, F2, 48) (dual of [606, 372, 49]-code), using 51 step Varšamov–Edel lengthening with (ri) = (5, 2, 2, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0) based on linear OA(2209, 530, F2, 48) (dual of [530, 321, 49]-code), using
- 1 times truncation [i] based on linear OA(2210, 531, F2, 49) (dual of [531, 321, 50]-code), using
- construction XX applied to C1 = C([509,44]), C2 = C([0,46]), C3 = C1 + C2 = C([0,44]), and C∩ = C1 ∩ C2 = C([509,46]) [i] based on
- linear OA(2199, 511, F2, 47) (dual of [511, 312, 48]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,44}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(2199, 511, F2, 47) (dual of [511, 312, 48]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,46], and designed minimum distance d ≥ |I|+1 = 48 [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 = {−2,−1,…,46}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(2190, 511, F2, 45) (dual of [511, 321, 46]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,44], and designed minimum distance d ≥ |I|+1 = 46 [i]
- 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
- linear OA(21, 10, F2, 1) (dual of [10, 9, 2]-code) (see above)
- construction XX applied to C1 = C([509,44]), C2 = C([0,46]), C3 = C1 + C2 = C([0,44]), and C∩ = C1 ∩ C2 = C([509,46]) [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(2235, 607, F2, 49) (dual of [607, 372, 50]-code) | [i] | Adding a Parity Check Bit | |