Information on Result #1535554
Linear OOA(4103, 49055, F4, 3, 16) (dual of [(49055, 3), 147062, 17]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4103, 49055, F4, 16) (dual of [49055, 48952, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(4103, 65567, F4, 16) (dual of [65567, 65464, 17]-code), using
- 1 times truncation [i] based on linear OA(4104, 65568, F4, 17) (dual of [65568, 65464, 18]-code), using
- construction XX applied to Ce(16) ⊂ Ce(12) ⊂ Ce(10) [i] based on
- linear OA(497, 65536, F4, 17) (dual of [65536, 65439, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(473, 65536, F4, 13) (dual of [65536, 65463, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(465, 65536, F4, 11) (dual of [65536, 65471, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(45, 30, F4, 3) (dual of [30, 25, 4]-code or 30-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- linear OA(41, 2, F4, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(16) ⊂ Ce(12) ⊂ Ce(10) [i] based on
- 1 times truncation [i] based on linear OA(4104, 65568, F4, 17) (dual of [65568, 65464, 18]-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(4103, 16351, F4, 21, 16) (dual of [(16351, 21), 343268, 17]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |