Information on Result #1540686
Linear OOA(4192, 4194310, F4, 3, 21) (dual of [(4194310, 3), 12582738, 22]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(4192, 4194310, F4, 2, 21) (dual of [(4194310, 2), 8388428, 22]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(411, 9, F4, 2, 10) (dual of [(9, 2), 7, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,7P) [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- the Hermitian function field over F4 [i]
- extended algebraic-geometric NRT-code AGe(2;F,7P) [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- linear OOA(4181, 4194301, F4, 2, 21) (dual of [(4194301, 2), 8388421, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4181, 8388602, F4, 21) (dual of [8388602, 8388421, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4181, large, F4, 21) (dual of [large, large−181, 22]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(4181, large, F4, 21) (dual of [large, large−181, 22]-code), using
- OOA 2-folding [i] based on linear OA(4181, 8388602, F4, 21) (dual of [8388602, 8388421, 22]-code), using
- linear OOA(411, 9, F4, 2, 10) (dual of [(9, 2), 7, 11]-NRT-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(4192, 1048577, F4, 27, 21) (dual of [(1048577, 27), 28311387, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |