Information on Result #1324282
Linear OA(4259, 1048657, F4, 32) (dual of [1048657, 1048398, 33]-code), using construction X with Varšamov bound based on
- linear OA(4255, 1048651, F4, 32) (dual of [1048651, 1048396, 33]-code), using
- 1 times truncation [i] based on linear OA(4256, 1048652, F4, 33) (dual of [1048652, 1048396, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,12]) [i] based on
- linear OA(4241, 1048577, F4, 33) (dual of [1048577, 1048336, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(4181, 1048577, F4, 25) (dual of [1048577, 1048396, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [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 C([0,16]) ⊂ C([0,12]) [i] based on
- 1 times truncation [i] based on linear OA(4256, 1048652, F4, 33) (dual of [1048652, 1048396, 34]-code), using
- linear OA(4255, 1048653, F4, 29) (dual of [1048653, 1048398, 30]-code), using Gilbert–Varšamov bound and bm = 4255 > Vbs−1(k−1) = 283 648526 806167 845400 229365 137739 712852 803475 603311 850757 631854 841195 282068 661294 616223 601123 020329 349086 383389 549953 321615 069578 675848 654734 833096 481744 [i]
- linear OA(42, 4, F4, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,4)), using
- Reed–Solomon code RS(2,4) [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(4259, 524328, F4, 2, 32) (dual of [(524328, 2), 1048397, 33]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(4259, 349552, F4, 3, 32) (dual of [(349552, 3), 1048397, 33]-NRT-code) | [i] | ||