Information on Result #735174
Linear OA(8177, 6681, F81, 30) (dual of [6681, 6604, 31]-code), using (u, u+v)-construction based on
- linear OA(8118, 118, F81, 15) (dual of [118, 100, 16]-code), using
- construction X applied to AG(F,99P) ⊂ AG(F,101P) [i] based on
- linear OA(8117, 115, F81, 15) (dual of [115, 98, 16]-code), using algebraic-geometric code AG(F,99P) [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- linear OA(8115, 115, F81, 13) (dual of [115, 100, 14]-code), using algebraic-geometric code AG(F,101P) [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116 (see above)
- linear OA(811, 3, F81, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to AG(F,99P) ⊂ AG(F,101P) [i] based on
- linear OA(8159, 6563, F81, 30) (dual of [6563, 6504, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(28) [i] based on
- linear OA(8159, 6561, F81, 30) (dual of [6561, 6502, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(8157, 6561, F81, 29) (dual of [6561, 6504, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(29) ⊂ Ce(28) [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(8177, 2227, F81, 3, 30) (dual of [(2227, 3), 6604, 31]-NRT-code) | [i] | OOA Folding | |