Information on Result #1324014
Linear OA(4186, 65602, F4, 29) (dual of [65602, 65416, 30]-code), using construction X with Varšamov bound based on
- linear OA(4183, 65598, F4, 29) (dual of [65598, 65415, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(20) [i] based on
- linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4121, 65536, F4, 21) (dual of [65536, 65415, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(414, 62, F4, 7) (dual of [62, 48, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- a “GraXX†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- construction X applied to Ce(28) ⊂ Ce(20) [i] based on
- linear OA(4183, 65599, F4, 26) (dual of [65599, 65416, 27]-code), using Gilbert–Varšamov bound and bm = 4183 > Vbs−1(k−1) = 143786 937990 567181 956957 542392 582937 078275 501893 171838 860273 732202 640190 164601 285229 493893 982379 582455 697643 [i]
- linear OA(42, 3, F4, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,4)), using
- dual of repetition code with length 3 [i]
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(4186, 32801, F4, 2, 29) (dual of [(32801, 2), 65416, 30]-NRT-code) | [i] | OOA Folding | |