Information on Result #1300198
Linear OA(4136, 167, F4, 72) (dual of [167, 31, 73]-code), using construction X with Varšamov bound based on
- linear OA(4135, 165, F4, 72) (dual of [165, 30, 73]-code), using
- 3 times truncation [i] based on linear OA(4138, 168, F4, 75) (dual of [168, 30, 76]-code), using
- concatenation of two codes [i] 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
- linear OA(6418, 28, F64, 18) (dual of [28, 10, 19]-code or 28-arc in PG(17,64)), using
- concatenation of two codes [i] based on
- 3 times truncation [i] based on linear OA(4138, 168, F4, 75) (dual of [168, 30, 76]-code), using
- linear OA(4135, 166, F4, 71) (dual of [166, 31, 72]-code), using Gilbert–Varšamov bound and bm = 4135 > Vbs−1(k−1) = 1445 994932 487951 446371 309153 545159 071816 579369 357390 566819 026250 267201 823859 878176 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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.
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(4137, 169, F4, 72) (dual of [169, 32, 73]-code) | [i] | Construction X with Varšamov Bound | |