Information on Result #1561486
Linear OOA(9111, 4783003, F9, 3, 17) (dual of [(4783003, 3), 14348898, 18]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(9111, 4783003, F9, 17) (dual of [4783003, 4782892, 18]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(9110, 4783001, F9, 17) (dual of [4783001, 4782891, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- linear OA(9106, 4782969, F9, 17) (dual of [4782969, 4782863, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(978, 4782969, F9, 13) (dual of [4782969, 4782891, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(94, 32, F9, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,9)), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- linear OA(9110, 4783002, F9, 16) (dual of [4783002, 4782892, 17]-code), using Gilbert–Varšamov bound and bm = 9110 > Vbs−1(k−1) = 422034 451883 037198 745147 407448 575628 556722 525695 672473 399458 292135 467570 013889 673550 996053 166224 420809 [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(9110, 4783001, F9, 17) (dual of [4783001, 4782891, 18]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(9111, 1594334, F9, 21, 17) (dual of [(1594334, 21), 33480903, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |