Information on Result #686065
Linear OA(727, 56, F7, 16) (dual of [56, 29, 17]-code), using construction X applied to Ce(15) ⊂ Ce(11) based on
- linear OA(724, 49, F7, 16) (dual of [49, 25, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(720, 49, F7, 12) (dual of [49, 29, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(73, 7, F7, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,7) or 7-cap in PG(2,7)), using
- Reed–Solomon code RS(4,7) [i]
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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(726, 55, F7, 15) (dual of [55, 29, 16]-code) | [i] | Truncation | |
| 2 | Linear OOA(727, 28, F7, 2, 16) (dual of [(28, 2), 29, 17]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(727, 18, F7, 3, 16) (dual of [(18, 3), 27, 17]-NRT-code) | [i] | ||