Information on Result #686270
Linear OA(879, 2097168, F8, 13) (dual of [2097168, 2097089, 14]-code), using construction X4 applied to Ce(12) ⊂ Ce(10) based on
- linear OA(878, 2097152, F8, 13) (dual of [2097152, 2097074, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(864, 2097152, F8, 11) (dual of [2097152, 2097088, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(815, 16, F8, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,8)), using
- dual of repetition code with length 16 [i]
- linear OA(81, 16, F8, 1) (dual of [16, 15, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-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(880, 2097169, F8, 13) (dual of [2097169, 2097089, 14]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(880, 2097170, F8, 13) (dual of [2097170, 2097090, 14]-code) | [i] | Construction X with Varšamov Bound | |
| 3 | Linear OOA(879, 1048584, F8, 2, 13) (dual of [(1048584, 2), 2097089, 14]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(879, 699056, F8, 3, 13) (dual of [(699056, 3), 2097089, 14]-NRT-code) | [i] | ||