Information on Result #1324390
Linear OA(9131, 59090, F9, 28) (dual of [59090, 58959, 29]-code), using construction X with Varšamov bound based on
- linear OA(9130, 59088, F9, 28) (dual of [59088, 58958, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(20) [i] based on
- linear OA(9121, 59049, F9, 28) (dual of [59049, 58928, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(991, 59049, F9, 21) (dual of [59049, 58958, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(99, 39, F9, 6) (dual of [39, 30, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(99, 41, F9, 6) (dual of [41, 32, 7]-code), using
- a “GraCyc†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(99, 41, F9, 6) (dual of [41, 32, 7]-code), using
- construction X applied to Ce(27) ⊂ Ce(20) [i] based on
- linear OA(9130, 59089, F9, 27) (dual of [59089, 58959, 28]-code), using Gilbert–Varšamov bound and bm = 9130 > Vbs−1(k−1) = 8 537623 522245 579710 858375 579730 972001 592903 076995 397879 098520 791818 555281 521693 535508 683948 336209 605356 515944 973310 827649 [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
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(9131, 59090, F9, 2, 28) (dual of [(59090, 2), 118049, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(9131, 59090, F9, 3, 28) (dual of [(59090, 3), 177139, 29]-NRT-code) | [i] | ||
| 3 | Digital (103, 131, 59090)-net over F9 | [i] | ||
| 4 | Linear OOA(9131, 29545, F9, 2, 28) (dual of [(29545, 2), 58959, 29]-NRT-code) | [i] | OOA Folding | |