Information on Result #904623
Linear OOA(8178, 265922, F81, 2, 21) (dual of [(265922, 2), 531766, 22]-NRT-code), using (u, u+v)-construction based on
- linear OOA(8117, 200, F81, 2, 10) (dual of [(200, 2), 383, 11]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(816, 100, F81, 2, 5) (dual of [(100, 2), 194, 6]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,194P) [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- linear OOA(8111, 100, F81, 2, 10) (dual of [(100, 2), 189, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,189P) [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100 (see above)
- linear OOA(816, 100, F81, 2, 5) (dual of [(100, 2), 194, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(8161, 265722, F81, 2, 21) (dual of [(265722, 2), 531383, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8161, 531444, F81, 21) (dual of [531444, 531383, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- linear OA(8161, 531441, F81, 21) (dual of [531441, 531380, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(8158, 531441, F81, 20) (dual of [531441, 531383, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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, using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- OOA 2-folding [i] based on linear OA(8161, 531444, F81, 21) (dual of [531444, 531383, 22]-code), 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(8178, 132961, F81, 4, 21) (dual of [(132961, 4), 531766, 22]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(8178, 53184, F81, 22, 21) (dual of [(53184, 22), 1169970, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |