Information on Result #637259
Linear OA(4138, 168, F4, 75) (dual of [168, 30, 76]-code), using concatenation of two codes based on
- linear OA(6418, 28, F64, 18) (dual of [28, 10, 19]-code or 28-arc in PG(17,64)), using
- discarding factors / shortening the dual code based on linear OA(6418, 64, F64, 18) (dual of [64, 46, 19]-code or 64-arc in PG(17,64)), using
- Reed–Solomon code RS(46,64) [i]
- discarding factors / shortening the dual code based on linear OA(6418, 64, F64, 18) (dual of [64, 46, 19]-code or 64-arc in PG(17,64)), using
- linear OA(43, 6, F4, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,4) or 6-cap in PG(2,4)), 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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(4138, 168, F4, 74) (dual of [168, 30, 75]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(4138, 168, F4, 73) (dual of [168, 30, 74]-code) | [i] | ||
| 3 | Linear OA(4139, 169, F4, 75) (dual of [169, 30, 76]-code) | [i] | Code Embedding in Larger Space | |
| 4 | Linear OA(4137, 167, F4, 74) (dual of [167, 30, 75]-code) | [i] | Truncation | |
| 5 | Linear OA(4136, 166, F4, 73) (dual of [166, 30, 74]-code) | [i] | ||
| 6 | Linear OA(4135, 165, F4, 72) (dual of [165, 30, 73]-code) | [i] | ||
| 7 | Linear OA(4134, 164, F4, 71) (dual of [164, 30, 72]-code) | [i] | ||
| 8 | Linear OA(4133, 163, F4, 70) (dual of [163, 30, 71]-code) | [i] | ||
| 9 | Linear OA(4131, 161, F4, 68) (dual of [161, 30, 69]-code) | [i] | ||
| 10 | Linear OOA(4138, 84, F4, 2, 75) (dual of [(84, 2), 30, 76]-NRT-code) | [i] | OOA Folding | |
| 11 | Linear OOA(4138, 56, F4, 3, 75) (dual of [(56, 3), 30, 76]-NRT-code) | [i] | ||