Information on Result #686165
Linear OA(746, 72, F7, 24) (dual of [72, 26, 25]-code), using construction XX applied to Ce(23) ⊂ Ce(16) ⊂ Ce(12) based on
- 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(725, 49, F7, 17) (dual of [49, 24, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(722, 49, F7, 13) (dual of [49, 27, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(78, 18, F7, 6) (dual of [18, 10, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(78, 19, F7, 6) (dual of [19, 11, 7]-code), using
- linear OA(73, 5, F7, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,7) or 5-cap in PG(2,7)), using
- discarding factors / shortening the dual code based on 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]
- discarding factors / shortening the dual code based on 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
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(746, 24, F7, 3, 24) (dual of [(24, 3), 26, 25]-NRT-code) | [i] | OOA Folding | |