Information on Result #2243662
Linear OA(4142, 4194358, F4, 16) (dual of [4194358, 4194216, 17]-code), using 1 times truncation based on linear OA(4143, 4194359, F4, 17) (dual of [4194359, 4194216, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,5]) [i] based on
- linear OA(4133, 4194305, F4, 17) (dual of [4194305, 4194172, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4194305 | 422−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(489, 4194305, F4, 11) (dual of [4194305, 4194216, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 4194305 | 422−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(410, 54, F4, 5) (dual of [54, 44, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
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(4142, 2333129, F4, 2, 16) (dual of [(2333129, 2), 4666116, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4142, 2333129, F4, 3, 16) (dual of [(2333129, 3), 6999245, 17]-NRT-code) | [i] | ||
| 3 | Digital (126, 142, 2333129)-net over F4 | [i] | ||
| 4 | Linear OOA(4142, 2097179, F4, 2, 16) (dual of [(2097179, 2), 4194216, 17]-NRT-code) | [i] | OOA Folding | |