Information on Result #702378
Linear OA(2194, 576, F2, 40) (dual of [576, 382, 41]-code), using construction XX applied to C1 = C([505,28]), C2 = C([0,34]), C3 = C1 + C2 = C([0,28]), and C∩ = C1 ∩ C2 = C([505,34]) based on
- linear OA(2154, 511, F2, 35) (dual of [511, 357, 36]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−6,−5,…,28}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(2145, 511, F2, 35) (dual of [511, 366, 36]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,34], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(2172, 511, F2, 41) (dual of [511, 339, 42]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−6,−5,…,34}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(2127, 511, F2, 29) (dual of [511, 384, 30]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,28], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(211, 36, F2, 4) (dual of [36, 25, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(211, 44, F2, 4) (dual of [44, 33, 5]-code), using
- 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
Mode: Constructive and 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(2195, 577, F2, 41) (dual of [577, 382, 42]-code) | [i] | Adding a Parity Check Bit | |
| 2 | Linear OOA(2194, 288, F2, 2, 40) (dual of [(288, 2), 382, 41]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2194, 192, F2, 3, 40) (dual of [(192, 3), 382, 41]-NRT-code) | [i] | ||
| 4 | Linear OOA(2194, 144, F2, 4, 40) (dual of [(144, 4), 382, 41]-NRT-code) | [i] | ||