Information on Result #1300444
Linear OA(4172, 1048628, F4, 22) (dual of [1048628, 1048456, 23]-code), using construction X with Varšamov bound based on
- linear OA(4169, 1048624, F4, 22) (dual of [1048624, 1048455, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(4161, 1048576, F4, 22) (dual of [1048576, 1048415, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(4121, 1048576, F4, 17) (dual of [1048576, 1048455, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(48, 48, F4, 4) (dual of [48, 40, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(48, 85, F4, 4) (dual of [85, 77, 5]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(4169, 1048625, F4, 19) (dual of [1048625, 1048456, 20]-code), using Gilbert–Varšamov bound and bm = 4169 > Vbs−1(k−1) = 142212 235006 563922 839139 666108 846364 350768 034545 397462 659863 095697 008311 245514 713911 944010 145374 856442 [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(4172, 524314, F4, 2, 22) (dual of [(524314, 2), 1048456, 23]-NRT-code) | [i] | OOA Folding | |