Information on Result #731324
Linear OA(8172, 524304, F8, 29) (dual of [524304, 524132, 30]-code), using trace code based on linear OA(6486, 262152, F64, 29) (dual of [262152, 262066, 30]-code), using
- construction X applied to C([0,14]) ⊂ C([0,13]) [i] based on
- linear OA(6485, 262145, F64, 29) (dual of [262145, 262060, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(6479, 262145, F64, 27) (dual of [262145, 262066, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(641, 7, F64, 1) (dual of [7, 6, 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(8173, 524305, F8, 29) (dual of [524305, 524132, 30]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8172, 262152, F8, 2, 29) (dual of [(262152, 2), 524132, 30]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(8172, 174768, F8, 3, 29) (dual of [(174768, 3), 524132, 30]-NRT-code) | [i] | ||
| 4 | Linear OOA(8172, 37450, F8, 29, 29) (dual of [(37450, 29), 1085878, 30]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |