Information on Result #1324150
Linear OA(4230, 1048656, F4, 29) (dual of [1048656, 1048426, 30]-code), using construction X with Varšamov bound based on
- linear OA(4226, 1048651, F4, 29) (dual of [1048651, 1048425, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(20) [i] based on
- linear OA(4211, 1048576, F4, 29) (dual of [1048576, 1048365, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4151, 1048576, F4, 21) (dual of [1048576, 1048425, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(415, 75, F4, 7) (dual of [75, 60, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(415, 85, F4, 7) (dual of [85, 70, 8]-code), using
- construction X applied to Ce(28) ⊂ Ce(20) [i] based on
- linear OA(4226, 1048652, F4, 25) (dual of [1048652, 1048426, 26]-code), using Gilbert–Varšamov bound and bm = 4226 > Vbs−1(k−1) = 1 423104 720354 811191 215501 369378 276469 331370 277317 044736 250116 254943 054520 065912 938139 304984 741824 381590 908350 794749 196814 229617 059924 [i]
- linear OA(43, 4, F4, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,4) or 4-cap in PG(2,4)), using
- dual of repetition code with length 4 [i]
- Reed–Solomon code RS(1,4) [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(4230, 524328, F4, 2, 29) (dual of [(524328, 2), 1048426, 30]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(4230, 349552, F4, 3, 29) (dual of [(349552, 3), 1048426, 30]-NRT-code) | [i] | ||