Information on Result #1560178
Linear OOA(971, 531464, F9, 3, 13) (dual of [(531464, 3), 1594321, 14]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(971, 531464, F9, 13) (dual of [531464, 531393, 14]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(970, 531462, F9, 13) (dual of [531462, 531392, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- 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(949, 531441, F9, 10) (dual of [531441, 531392, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(93, 21, F9, 2) (dual of [21, 18, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(970, 531463, F9, 12) (dual of [531463, 531393, 13]-code), using Gilbert–Varšamov bound and bm = 970 > Vbs−1(k−1) = 205581 822003 982870 126973 841916 675158 646034 660101 208825 881495 567345 [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(970, 531462, F9, 13) (dual of [531462, 531392, 14]-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(971, 265731, F9, 15, 13) (dual of [(265731, 15), 3985894, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |