Information on Result #1561281
Linear OOA(9106, 531482, F9, 3, 19) (dual of [(531482, 3), 1594340, 20]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(9106, 531482, F9, 19) (dual of [531482, 531376, 20]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(9104, 531478, F9, 19) (dual of [531478, 531374, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(12) [i] based on
- linear OA(997, 531441, F9, 19) (dual of [531441, 531344, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(967, 531441, F9, 13) (dual of [531441, 531374, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(97, 37, F9, 5) (dual of [37, 30, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- construction X applied to Ce(18) ⊂ Ce(12) [i] based on
- linear OA(9104, 531480, F9, 18) (dual of [531480, 531376, 19]-code), using Gilbert–Varšamov bound and bm = 9104 > Vbs−1(k−1) = 136 337624 831161 448362 005612 235322 875092 079314 504022 616837 598118 105615 078081 767008 252949 492945 806841 [i]
- linear OA(90, 2, F9, 0) (dual of [2, 2, 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(9104, 531478, F9, 19) (dual of [531478, 531374, 20]-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(9106, 177160, F9, 21, 19) (dual of [(177160, 21), 3720254, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |