Information on Result #1450701
Linear OOA(9104, 4783003, F9, 2, 16) (dual of [(4783003, 2), 9565902, 17]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(9104, 4783003, F9, 16) (dual of [4783003, 4782899, 17]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(9103, 4783001, F9, 16) (dual of [4783001, 4782898, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- linear OA(999, 4782969, F9, 16) (dual of [4782969, 4782870, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(971, 4782969, F9, 12) (dual of [4782969, 4782898, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(15) ⊂ Ce(11) [i] based on
- linear OA(9103, 4783002, F9, 15) (dual of [4783002, 4782899, 16]-code), using Gilbert–Varšamov bound and bm = 9103 > Vbs−1(k−1) = 165443 597609 647893 113599 597270 670656 805468 819771 675350 475869 186864 992491 664042 988548 512222 654409 [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(9103, 4783001, F9, 16) (dual of [4783001, 4782898, 17]-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(9104, 2391501, F9, 3, 16) (dual of [(2391501, 3), 7174399, 17]-NRT-code) | [i] | OOA Folding | |