Information on Result #737739
Linear OA(7107, 16861, F7, 22) (dual of [16861, 16754, 23]-code), using construction X applied to Ce(21) ⊂ Ce(11) based on
- linear OA(791, 16807, F7, 22) (dual of [16807, 16716, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(751, 16807, F7, 12) (dual of [16807, 16756, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(716, 54, F7, 9) (dual of [54, 38, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(5) [i] based on
- linear OA(714, 49, F7, 9) (dual of [49, 35, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(711, 49, F7, 6) (dual of [49, 38, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(72, 5, F7, 2) (dual of [5, 3, 3]-code or 5-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(8) ⊂ Ce(5) [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(7107, 8430, F7, 2, 22) (dual of [(8430, 2), 16753, 23]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(7107, 5620, F7, 3, 22) (dual of [(5620, 3), 16753, 23]-NRT-code) | [i] | ||