Information on Result #1561974
Linear OOA(9122, 4783015, F9, 3, 19) (dual of [(4783015, 3), 14348923, 20]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(9122, 4783015, F9, 19) (dual of [4783015, 4782893, 20]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(9120, 4783011, F9, 19) (dual of [4783011, 4782891, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(12) [i] based on
- linear OA(9113, 4782969, F9, 19) (dual of [4782969, 4782856, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(97, 42, F9, 5) (dual of [42, 35, 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(9120, 4783013, F9, 18) (dual of [4783013, 4782893, 19]-code), using Gilbert–Varšamov bound and bm = 9120 > Vbs−1(k−1) = 2 271820 979786 716051 824536 673470 408417 084553 375315 031398 533400 827447 232085 368185 227728 375755 193646 017289 000316 101281 [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(9120, 4783011, F9, 19) (dual of [4783011, 4782891, 20]-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(9122, 1594338, F9, 21, 19) (dual of [(1594338, 21), 33480976, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |