Information on Result #1027508
Linear OOA(4167, 57, F4, 3, 144) (dual of [(57, 3), 4, 145]-NRT-code), using juxtaposition based on
- linear OOA(420, 8, F4, 3, 19) (dual of [(8, 3), 4, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(420, 9, F4, 3, 19) (dual of [(9, 3), 7, 20]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;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(3;F,7P) [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- discarding factors / shortening the dual code based on linear OOA(420, 9, F4, 3, 19) (dual of [(9, 3), 7, 20]-NRT-code), using
- linear OOA(4143, 49, F4, 3, 124) (dual of [(49, 3), 4, 125]-NRT-code), using
- juxtaposition [i] based on
- linear OOA(417, 7, F4, 3, 16) (dual of [(7, 3), 4, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(417, 9, F4, 3, 16) (dual of [(9, 3), 10, 17]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,10P) [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9 (see above)
- discarding factors / shortening the dual code based on linear OOA(417, 9, F4, 3, 16) (dual of [(9, 3), 10, 17]-NRT-code), using
- linear OOA(4122, 42, F4, 3, 107) (dual of [(42, 3), 4, 108]-NRT-code), using
- repeating each code word 3 times [i] based on linear OOA(438, 14, F4, 3, 35) (dual of [(14, 3), 4, 36]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,6P) [i] based on function field F/F4 with g(F) = 3 and N(F) ≥ 14, using
- repeating each code word 3 times [i] based on linear OOA(438, 14, F4, 3, 35) (dual of [(14, 3), 4, 36]-NRT-code), using
- linear OOA(417, 7, F4, 3, 16) (dual of [(7, 3), 4, 17]-NRT-code), using
- juxtaposition [i] based on
Mode: Constructive and 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(4167, 57, F4, 3, 143) (dual of [(57, 3), 4, 144]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(4167, 57, F4, 3, 142) (dual of [(57, 3), 4, 143]-NRT-code) | [i] | ||
| 3 | Linear OOA(4167, 57, F4, 3, 141) (dual of [(57, 3), 4, 142]-NRT-code) | [i] | ||
| 4 | Linear OOA(4167, 57, F4, 3, 140) (dual of [(57, 3), 4, 141]-NRT-code) | [i] | ||
| 5 | Linear OOA(4167, 57, F4, 3, 139) (dual of [(57, 3), 4, 140]-NRT-code) | [i] | ||
| 6 | Linear OOA(4167, 57, F4, 3, 138) (dual of [(57, 3), 4, 139]-NRT-code) | [i] | ||