Information on Result #735458
Linear OA(8143, 531610, F81, 12) (dual of [531610, 531567, 13]-code), using (u, u+v)-construction based on
- linear OA(819, 166, F81, 6) (dual of [166, 157, 7]-code), using
- construction X applied to C([38,43]) ⊂ C([39,43]) [i] based on
- linear OA(819, 164, F81, 6) (dual of [164, 155, 7]-code), using the BCH-code C(I) with length 164 | 812−1, defining interval I = {38,39,…,43}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(817, 164, F81, 5) (dual of [164, 157, 6]-code), using the BCH-code C(I) with length 164 | 812−1, defining interval I = {39,40,41,42,43}, and designed minimum distance d ≥ |I|+1 = 6 [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 C([38,43]) ⊂ C([39,43]) [i] based on
- linear OA(8134, 531444, F81, 12) (dual of [531444, 531410, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(8134, 531441, F81, 12) (dual of [531441, 531407, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(8131, 531441, F81, 11) (dual of [531441, 531410, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(810, 3, F81, 0) (dual of [3, 3, 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 (see above)
- construction X applied to Ce(11) ⊂ Ce(10) [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(8143, 265805, F81, 2, 12) (dual of [(265805, 2), 531567, 13]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(8143, 177203, F81, 3, 12) (dual of [(177203, 3), 531566, 13]-NRT-code) | [i] | ||