Information on Result #1538053
Linear OOA(4153, 524299, F4, 3, 20) (dual of [(524299, 3), 1572744, 21]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(4153, 524299, F4, 2, 20) (dual of [(524299, 2), 1048445, 21]-NRT-code), using
- 41 times duplication [i] based on linear OOA(4152, 524299, F4, 2, 20) (dual of [(524299, 2), 1048446, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4152, 1048598, F4, 20) (dual of [1048598, 1048446, 21]-code), using
- construction X4 applied to Ce(20) ⊂ Ce(17) [i] based on
- 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(4131, 1048576, F4, 18) (dual of [1048576, 1048445, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(421, 22, F4, 21) (dual of [22, 1, 22]-code or 22-arc in PG(20,4)), using
- dual of repetition code with length 22 [i]
- linear OA(41, 22, F4, 1) (dual of [22, 21, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(20) ⊂ Ce(17) [i] based on
- OOA 2-folding [i] based on linear OA(4152, 1048598, F4, 20) (dual of [1048598, 1048446, 21]-code), 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(4153, 131074, F4, 27, 20) (dual of [(131074, 27), 3538845, 21]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |