Information on Result #735221
Linear OA(8178, 13126, F81, 27) (dual of [13126, 13048, 28]-code), using (u, u+v)-construction based on
- linear OA(8125, 6563, F81, 13) (dual of [6563, 6538, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- linear OA(8125, 6561, F81, 13) (dual of [6561, 6536, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(8123, 6561, F81, 12) (dual of [6561, 6538, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(810, 2, F81, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- linear OA(8153, 6563, F81, 27) (dual of [6563, 6510, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- linear OA(8153, 6561, F81, 27) (dual of [6561, 6508, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(8151, 6561, F81, 26) (dual of [6561, 6510, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(810, 2, F81, 0) (dual of [2, 2, 1]-code) (see above)
- construction X applied to Ce(26) ⊂ Ce(25) [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 OOA(8178, 6563, F81, 2, 27) (dual of [(6563, 2), 13048, 28]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(8178, 4375, F81, 3, 27) (dual of [(4375, 3), 13047, 28]-NRT-code) | [i] | ||