Information on Result #1451898
Linear OOA(9131, 13128, F9, 2, 33) (dual of [(13128, 2), 26125, 34]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(9131, 13128, F9, 33) (dual of [13128, 12997, 34]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(9130, 13126, F9, 33) (dual of [13126, 12996, 34]-code), using
- trace code [i] based on linear OA(8165, 6563, F81, 33) (dual of [6563, 6498, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(31) [i] based on
- linear OA(8165, 6561, F81, 33) (dual of [6561, 6496, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(8163, 6561, F81, 32) (dual of [6561, 6498, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [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(32) ⊂ Ce(31) [i] based on
- trace code [i] based on linear OA(8165, 6563, F81, 33) (dual of [6563, 6498, 34]-code), using
- linear OA(9130, 13127, F9, 32) (dual of [13127, 12997, 33]-code), using Gilbert–Varšamov bound and bm = 9130 > Vbs−1(k−1) = 53 407660 739261 997504 274970 375037 969563 571616 059301 421379 604995 101040 737510 936890 862782 721517 617809 435619 020509 039557 389809 [i]
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(9130, 13126, F9, 33) (dual of [13126, 12996, 34]-code), using
Mode: 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(9131, 6564, F9, 3, 33) (dual of [(6564, 3), 19561, 34]-NRT-code) | [i] | OOA Folding | |