Information on Result #1539011
Linear OOA(4168, 1810337, F4, 3, 20) (dual of [(1810337, 3), 5430843, 21]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(4168, 1810337, F4, 2, 20) (dual of [(1810337, 2), 3620506, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4168, 2097164, F4, 2, 20) (dual of [(2097164, 2), 4194160, 21]-NRT-code), using
- 41 times duplication [i] based on linear OOA(4167, 2097164, F4, 2, 20) (dual of [(2097164, 2), 4194161, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4167, 4194328, F4, 20) (dual of [4194328, 4194161, 21]-code), using
- construction X4 applied to Ce(20) ⊂ Ce(17) [i] based on
- linear OA(4166, 4194304, F4, 21) (dual of [4194304, 4194138, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(4144, 4194304, F4, 18) (dual of [4194304, 4194160, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(423, 24, F4, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,4)), using
- dual of repetition code with length 24 [i]
- linear OA(41, 24, F4, 1) (dual of [24, 23, 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(4167, 4194328, F4, 20) (dual of [4194328, 4194161, 21]-code), using
- 41 times duplication [i] based on linear OOA(4167, 2097164, F4, 2, 20) (dual of [(2097164, 2), 4194161, 21]-NRT-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(4168, 452584, F4, 27, 20) (dual of [(452584, 27), 12219600, 21]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |