Information on Result #1451911
Linear OOA(9131, 4783023, F9, 2, 20) (dual of [(4783023, 2), 9565915, 21]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(9131, 4783023, F9, 20) (dual of [4783023, 4782892, 21]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(9130, 4783021, F9, 20) (dual of [4783021, 4782891, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(12) [i] based on
- linear OA(9120, 4782969, F9, 20) (dual of [4782969, 4782849, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(910, 52, F9, 6) (dual of [52, 42, 7]-code), using
- a “Gra†code from Grassl’s database [i]
- construction X applied to Ce(19) ⊂ Ce(12) [i] based on
- linear OA(9130, 4783022, F9, 19) (dual of [4783022, 4782892, 20]-code), using Gilbert–Varšamov bound and bm = 9130 > Vbs−1(k−1) = 4 829545 205077 712384 497437 400543 785330 576479 917009 669119 359789 170178 569226 306249 813553 188885 008592 351564 474955 545881 137385 [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(9130, 4783021, F9, 20) (dual of [4783021, 4782891, 21]-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(9131, 2391511, F9, 3, 20) (dual of [(2391511, 3), 7174402, 21]-NRT-code) | [i] | OOA Folding | |