Information on Result #686363
Linear OA(8166, 2097226, F8, 25) (dual of [2097226, 2097060, 26]-code), using construction X applied to Ce(24) ⊂ Ce(14) based on
- linear OA(8148, 2097152, F8, 25) (dual of [2097152, 2097004, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(892, 2097152, F8, 15) (dual of [2097152, 2097060, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(818, 74, F8, 9) (dual of [74, 56, 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(8167, 2097227, F8, 25) (dual of [2097227, 2097060, 26]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(8165, 2097225, F8, 24) (dual of [2097225, 2097060, 25]-code) | [i] | Truncation | |
| 3 | Linear OOA(8166, 1048613, F8, 2, 25) (dual of [(1048613, 2), 2097060, 26]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(8166, 699075, F8, 3, 25) (dual of [(699075, 3), 2097059, 26]-NRT-code) | [i] | ||