Information on Result #686140
Linear OA(757, 70, F7, 36) (dual of [70, 13, 37]-code), using construction XX applied to Ce(39) ⊂ Ce(26) ⊂ Ce(25) based on
- linear OA(745, 49, F7, 40) (dual of [49, 4, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(738, 49, F7, 27) (dual of [49, 11, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- 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(710, 19, F7, 8) (dual of [19, 9, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(710, 20, F7, 8) (dual of [20, 10, 9]-code), using
- extended quadratic residue code Qe(20,7) [i]
- discarding factors / shortening the dual code based on linear OA(710, 20, F7, 8) (dual of [20, 10, 9]-code), using
- linear OA(70, 2, F7, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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(757, 35, F7, 2, 36) (dual of [(35, 2), 13, 37]-NRT-code) | [i] | OOA Folding | |