Information on Result #675733
Linear OA(3229, 3289, F3, 44) (dual of [3289, 3060, 45]-code), using construction X applied to Ce(43) ⊂ Ce(42) based on
- linear OA(3229, 3281, F3, 44) (dual of [3281, 3052, 45]-code), using an extension Ce(43) of the narrow-sense BCH-code C(I) with length 3280 | 38−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(3221, 3281, F3, 43) (dual of [3281, 3060, 44]-code), using an extension Ce(42) of the narrow-sense BCH-code C(I) with length 3280 | 38−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(30, 8, F3, 0) (dual of [8, 8, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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 OA(3230, 3290, F3, 44) (dual of [3290, 3060, 45]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3230, 3291, F3, 44) (dual of [3291, 3061, 45]-code) | [i] | Construction X with Varšamov Bound | |
| 3 | Linear OA(3231, 3293, F3, 44) (dual of [3293, 3062, 45]-code) | [i] | ||
| 4 | Linear OA(3232, 3295, F3, 44) (dual of [3295, 3063, 45]-code) | [i] | ||
| 5 | Linear OOA(3229, 1644, F3, 2, 44) (dual of [(1644, 2), 3059, 45]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(3229, 1096, F3, 3, 44) (dual of [(1096, 3), 3059, 45]-NRT-code) | [i] | ||
| 7 | Linear OOA(3229, 822, F3, 4, 44) (dual of [(822, 4), 3059, 45]-NRT-code) | [i] | ||
| 8 | Linear OOA(3229, 657, F3, 5, 44) (dual of [(657, 5), 3056, 45]-NRT-code) | [i] | ||