Information on Result #731159
Linear OA(888, 8216, F8, 21) (dual of [8216, 8128, 22]-code), using trace code based on linear OA(6444, 4108, F64, 21) (dual of [4108, 4064, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(6441, 4097, F64, 21) (dual of [4097, 4056, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(6433, 4097, F64, 17) (dual of [4097, 4064, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(643, 11, F64, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,64) or 11-cap in PG(2,64)), using
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
- Reed–Solomon code RS(61,64) [i]
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), 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(889, 8217, F8, 21) (dual of [8217, 8128, 22]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(888, 4108, F8, 2, 21) (dual of [(4108, 2), 8128, 22]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(888, 2738, F8, 3, 21) (dual of [(2738, 3), 8126, 22]-NRT-code) | [i] | ||
| 4 | Linear OOA(888, 821, F8, 21, 21) (dual of [(821, 21), 17153, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |