Information on Result #686374
Linear OA(8159, 2097233, F8, 23) (dual of [2097233, 2097074, 24]-code), using construction X applied to Ce(22) ⊂ Ce(12) based on
- linear OA(8141, 2097152, F8, 23) (dual of [2097152, 2097011, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 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(818, 81, F8, 9) (dual of [81, 63, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(818, 130, F8, 9) (dual of [130, 112, 10]-code), using
- trace code [i] based on linear OA(649, 65, F64, 9) (dual of [65, 56, 10]-code or 65-arc in PG(8,64)), using
- extended Reed–Solomon code RSe(56,64) [i]
- the expurgated narrow-sense BCH-code C(I) with length 65 | 642−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- trace code [i] based on linear OA(649, 65, F64, 9) (dual of [65, 56, 10]-code or 65-arc in PG(8,64)), using
- discarding factors / shortening the dual code based on linear OA(818, 130, F8, 9) (dual of [130, 112, 10]-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(8160, 2097234, F8, 23) (dual of [2097234, 2097074, 24]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8159, 1048616, F8, 2, 23) (dual of [(1048616, 2), 2097073, 24]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(8159, 699077, F8, 3, 23) (dual of [(699077, 3), 2097072, 24]-NRT-code) | [i] | ||
| 4 | Linear OOA(8159, 190657, F8, 23, 23) (dual of [(190657, 23), 4384952, 24]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |