Information on Result #686161
Linear OA(741, 58, F7, 26) (dual of [58, 17, 27]-code), using construction XX applied to Ce(25) ⊂ Ce(23) ⊂ Ce(19) based on
- linear OA(736, 49, F7, 26) (dual of [49, 13, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(733, 49, F7, 24) (dual of [49, 16, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(731, 49, F7, 20) (dual of [49, 18, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(71, 5, F7, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, 7, F7, 1) (dual of [7, 6, 2]-code), using
- Reed–Solomon code RS(6,7) [i]
- discarding factors / shortening the dual code based on linear OA(71, 7, F7, 1) (dual of [7, 6, 2]-code), using
- linear OA(73, 4, F7, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,7) or 4-cap in PG(2,7)), using
- dual of repetition code with length 4 [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 OOA(741, 29, F7, 2, 26) (dual of [(29, 2), 17, 27]-NRT-code) | [i] | OOA Folding | |