Information on Result #697043
Linear OA(32107, 32814, F32, 33) (dual of [32814, 32707, 34]-code), using construction X applied to Ce(32) ⊂ Ce(20) based on
- linear OA(3294, 32768, F32, 33) (dual of [32768, 32674, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(3261, 32768, F32, 21) (dual of [32768, 32707, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(3213, 46, F32, 11) (dual of [46, 33, 12]-code), using
- construction X applied to AG(F,31P) ⊂ AG(F,33P) [i] based on
- linear OA(3212, 43, F32, 11) (dual of [43, 31, 12]-code), using algebraic-geometric code AG(F,31P) [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- linear OA(3210, 43, F32, 9) (dual of [43, 33, 10]-code), using algebraic-geometric code AG(F,33P) [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44 (see above)
- linear OA(321, 3, F32, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to AG(F,31P) ⊂ AG(F,33P) [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(32107, 32814, F32, 32) (dual of [32814, 32707, 33]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(32108, 32815, F32, 33) (dual of [32815, 32707, 34]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(32106, 32813, F32, 32) (dual of [32813, 32707, 33]-code) | [i] | Truncation | |
| 4 | Linear OOA(32107, 16407, F32, 2, 33) (dual of [(16407, 2), 32707, 34]-NRT-code) | [i] | OOA Folding | |