Information on Result #702351
Linear OA(2178, 554, F2, 39) (dual of [554, 376, 40]-code), using construction XX applied to C1 = C([475,510]), C2 = C([481,2]), C3 = C1 + C2 = C([481,510]), and C∩ = C1 ∩ C2 = C([475,2]) based on
- linear OA(2153, 511, F2, 36) (dual of [511, 358, 37]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−36,−35,…,−1}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(2145, 511, F2, 33) (dual of [511, 366, 34]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−30,−29,…,2}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(2163, 511, F2, 39) (dual of [511, 348, 40]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−36,−35,…,2}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(2135, 511, F2, 30) (dual of [511, 376, 31]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−30,−29,…,−1}, and designed minimum distance d ≥ |I|+1 = 31 [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(24, 14, F2, 2) (dual of [14, 10, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(24, 15, F2, 2) (dual of [15, 11, 3]-code), using
- Hamming code H(4,2) [i]
- discarding factors / shortening the dual code based on linear OA(24, 15, F2, 2) (dual of [15, 11, 3]-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(2177, 553, F2, 38) (dual of [553, 376, 39]-code) | [i] | Truncation | |