Information on Result #708759
Linear OA(4194, 1090, F4, 46) (dual of [1090, 896, 47]-code), using construction XX applied to C1 = C([301,340]), C2 = C([308,346]), C3 = C1 + C2 = C([308,340]), and C∩ = C1 ∩ C2 = C([301,346]) based on
- linear OA(4150, 1023, F4, 40) (dual of [1023, 873, 41]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {301,302,…,340}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(4146, 1023, F4, 39) (dual of [1023, 877, 40]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {308,309,…,346}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(4171, 1023, F4, 46) (dual of [1023, 852, 47]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {301,302,…,346}, and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(4125, 1023, F4, 33) (dual of [1023, 898, 34]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {308,309,…,340}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(413, 36, F4, 6) (dual of [36, 23, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- linear OA(410, 31, F4, 5) (dual of [31, 21, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 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(4195, 1091, F4, 46) (dual of [1091, 896, 47]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4194, 545, F4, 2, 46) (dual of [(545, 2), 896, 47]-NRT-code) | [i] | OOA Folding | |