Information on Result #731192
Linear OA(8108, 8204, F8, 27) (dual of [8204, 8096, 28]-code), using trace code based on linear OA(6454, 4102, F64, 27) (dual of [4102, 4048, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,12]) [i] based on
- linear OA(6453, 4097, F64, 27) (dual of [4097, 4044, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(6449, 4097, F64, 25) (dual of [4097, 4048, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(641, 5, F64, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(8109, 8205, F8, 27) (dual of [8205, 8096, 28]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8108, 4102, F8, 2, 27) (dual of [(4102, 2), 8096, 28]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(8108, 2734, F8, 3, 27) (dual of [(2734, 3), 8094, 28]-NRT-code) | [i] | ||
| 4 | Linear OOA(8108, 631, F8, 27, 27) (dual of [(631, 27), 16929, 28]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |