Information on Result #1324100
Linear OA(4215, 65623, F4, 32) (dual of [65623, 65408, 33]-code), using construction X with Varšamov bound based on
- linear OA(4214, 65621, F4, 32) (dual of [65621, 65407, 33]-code), using
- construction X applied to Ce(32) ⊂ Ce(21) [i] based on
- linear OA(4193, 65536, F4, 33) (dual of [65536, 65343, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(4129, 65536, F4, 22) (dual of [65536, 65407, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(421, 85, F4, 9) (dual of [85, 64, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(421, 86, F4, 9) (dual of [86, 65, 10]-code), using
- construction X applied to Ce(32) ⊂ Ce(21) [i] based on
- linear OA(4214, 65622, F4, 31) (dual of [65622, 65408, 32]-code), using Gilbert–Varšamov bound and bm = 4214 > Vbs−1(k−1) = 2 502936 050615 400529 190553 521166 057942 047489 632173 226640 437710 854803 543500 502033 266486 166211 686806 997824 652970 105706 716830 186336 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 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(4215, 65623, F4, 2, 32) (dual of [(65623, 2), 131031, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4215, 65623, F4, 3, 32) (dual of [(65623, 3), 196654, 33]-NRT-code) | [i] | ||
| 3 | Digital (183, 215, 65623)-net over F4 | [i] | ||
| 4 | Linear OOA(4215, 32811, F4, 2, 32) (dual of [(32811, 2), 65407, 33]-NRT-code) | [i] | OOA Folding | |