Information on Result #1324388
Linear OA(9124, 4783023, F9, 19) (dual of [4783023, 4782899, 20]-code), using construction X with Varšamov bound based on
- linear OA(9123, 4783021, F9, 19) (dual of [4783021, 4782898, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(11) [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(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(910, 52, F9, 6) (dual of [52, 42, 7]-code), using
- a “Gra†code from Grassl’s database [i]
- construction X applied to Ce(18) ⊂ Ce(11) [i] based on
- linear OA(9123, 4783022, F9, 18) (dual of [4783022, 4782899, 19]-code), using Gilbert–Varšamov bound and bm = 9123 > Vbs−1(k−1) = 2 271893 652490 570941 051437 963484 209563 300415 974246 692671 682874 376718 786719 916592 921890 343648 099451 363806 190183 698665 [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(9124, 4783023, F9, 2, 19) (dual of [(4783023, 2), 9565922, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(9124, 4783023, F9, 3, 19) (dual of [(4783023, 3), 14348945, 20]-NRT-code) | [i] | ||
| 3 | Digital (105, 124, 4783023)-net over F9 | [i] | ||