Information on Result #635669
Linear OA(4158, 260, F4, 63) (dual of [260, 102, 64]-code), using concatenation of two codes based on
- linear OA(6431, 65, F64, 31) (dual of [65, 34, 32]-code or 65-arc in PG(30,64)), using
- extended Reed–Solomon code RSe(34,64) [i]
- the expurgated narrow-sense BCH-code C(I) with length 65 | 642−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 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(4158, 260, F4, 62) (dual of [260, 102, 63]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(4159, 261, F4, 63) (dual of [261, 102, 64]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(4160, 262, F4, 63) (dual of [262, 102, 64]-code) | [i] | ||
| 4 | Linear OA(4161, 263, F4, 63) (dual of [263, 102, 64]-code) | [i] | ||
| 5 | Linear OA(4162, 264, F4, 63) (dual of [264, 102, 64]-code) | [i] | ||
| 6 | Linear OA(4157, 259, F4, 62) (dual of [259, 102, 63]-code) | [i] | Truncation | |
| 7 | Linear OOA(4158, 130, F4, 2, 63) (dual of [(130, 2), 102, 64]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(4158, 86, F4, 3, 63) (dual of [(86, 3), 100, 64]-NRT-code) | [i] | ||