Information on Result #737738
Linear OA(7105, 16857, F7, 22) (dual of [16857, 16752, 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(714, 50, F7, 9) (dual of [50, 36, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(7) [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(713, 49, F7, 8) (dual of [49, 36, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(70, 1, F7, 0) (dual of [1, 1, 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
- construction X applied to Ce(8) ⊂ Ce(7) [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 OA(7106, 16858, F7, 22) (dual of [16858, 16752, 23]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(7105, 8428, F7, 2, 22) (dual of [(8428, 2), 16751, 23]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(7105, 5619, F7, 3, 22) (dual of [(5619, 3), 16752, 23]-NRT-code) | [i] | ||