Information on Result #737821
Linear OA(8154, 32836, F8, 31) (dual of [32836, 32682, 32]-code), using construction X applied to Ce(30) ⊂ Ce(19) based on
- linear OA(8136, 32768, F8, 31) (dual of [32768, 32632, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(886, 32768, F8, 20) (dual of [32768, 32682, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(818, 68, F8, 10) (dual of [68, 50, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(818, 69, F8, 10) (dual of [69, 51, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- linear OA(816, 64, F8, 10) (dual of [64, 48, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(813, 64, F8, 7) (dual of [64, 51, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(82, 5, F8, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,8)), using
- discarding factors / shortening the dual code based on linear OA(82, 8, F8, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,8)), using
- Reed–Solomon code RS(6,8) [i]
- discarding factors / shortening the dual code based on linear OA(82, 8, F8, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,8)), using
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(818, 69, F8, 10) (dual of [69, 51, 11]-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(8155, 32837, F8, 31) (dual of [32837, 32682, 32]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8154, 16418, F8, 2, 31) (dual of [(16418, 2), 32682, 32]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(8154, 10945, F8, 3, 31) (dual of [(10945, 3), 32681, 32]-NRT-code) | [i] | ||
| 4 | Linear OOA(8154, 2189, F8, 31, 31) (dual of [(2189, 31), 67705, 32]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |