Information on Result #737744
Linear OA(7101, 16862, F7, 20) (dual of [16862, 16761, 21]-code), using construction X applied to Ce(19) ⊂ Ce(10) based on
- linear OA(786, 16807, F7, 20) (dual of [16807, 16721, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(746, 16807, F7, 11) (dual of [16807, 16761, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(715, 55, F7, 8) (dual of [55, 40, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(4) [i] based on
- linear OA(713, 49, F7, 8) (dual of [49, 36, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(79, 49, F7, 5) (dual of [49, 40, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(72, 6, F7, 2) (dual of [6, 4, 3]-code or 6-arc in PG(1,7)), using
- discarding factors / shortening the dual code based on linear OA(72, 7, F7, 2) (dual of [7, 5, 3]-code or 7-arc in PG(1,7)), using
- Reed–Solomon code RS(5,7) [i]
- discarding factors / shortening the dual code based on linear OA(72, 7, F7, 2) (dual of [7, 5, 3]-code or 7-arc in PG(1,7)), using
- construction X applied to Ce(7) ⊂ Ce(4) [i] based on
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 OOA(7101, 8431, F7, 2, 20) (dual of [(8431, 2), 16761, 21]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(7101, 5620, F7, 3, 20) (dual of [(5620, 3), 16759, 21]-NRT-code) | [i] | ||
| 3 | Linear OOA(7101, 1686, F7, 20, 20) (dual of [(1686, 20), 33619, 21]-NRT-code) | [i] | OA Folding and Stacking | |