Information on Result #657248
Linear OA(4921, 50, F49, 21) (dual of [50, 29, 22]-code or 50-arc in PG(20,49)), using algebraic-geometric code AG(F,14P) with degPÂ =Â 2 based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using the rational function field F49(x) [i]
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
- Extended Reed–Solomon Code [i]
- Expurgated Narrow-Sense BCH-Codes (BCH-Bound) [i]
- Algebraic-Geometric Codes Defined Using a Non-Rational Place [i]
- Algebraic-Geometric Codes Defined Using a Non-Rational Place [i]
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(742, 100, F7, 21) (dual of [100, 58, 22]-code) | [i] | Trace Code | |
| 2 | Linear OA(792, 150, F7, 43) (dual of [150, 58, 44]-code) | [i] | Concatenation of Two Codes | |
| 3 | Linear OA(4924, 53, F49, 23) (dual of [53, 29, 24]-code) | [i] | ✔ | Construction X with Algebraic-Geometric Codes |
| 4 | Linear OA(4922, 53, F49, 21) (dual of [53, 31, 22]-code) | [i] | ✔ | |
| 5 | Linear OA(4928, 57, F49, 25) (dual of [57, 29, 26]-code) | [i] | ✔ | |
| 6 | Linear OA(4924, 57, F49, 21) (dual of [57, 33, 22]-code) | [i] | ✔ | |
| 7 | Linear OA(4932, 61, F49, 27) (dual of [61, 29, 28]-code) | [i] | ✔ | |
| 8 | Linear OA(4926, 61, F49, 21) (dual of [61, 35, 22]-code) | [i] | ✔ | |
| 9 | Linear OA(4936, 65, F49, 29) (dual of [65, 29, 30]-code) | [i] | ✔ | |
| 10 | Linear OA(4928, 65, F49, 21) (dual of [65, 37, 22]-code) | [i] | ✔ | |
| 11 | Linear OA(4940, 69, F49, 31) (dual of [69, 29, 32]-code) | [i] | ✔ | |
| 12 | Linear OA(4930, 69, F49, 21) (dual of [69, 39, 22]-code) | [i] | ✔ | |
| 13 | Linear OA(4944, 73, F49, 33) (dual of [73, 29, 34]-code) | [i] | ✔ | |
| 14 | Linear OA(4948, 77, F49, 35) (dual of [77, 29, 36]-code) | [i] | ✔ | |
| 15 | Linear OA(4952, 81, F49, 37) (dual of [81, 29, 38]-code) | [i] | ✔ | |
| 16 | Linear OA(4926, 55, F49, 24) (dual of [55, 29, 25]-code) | [i] | ✔ | |
| 17 | Linear OA(4923, 55, F49, 21) (dual of [55, 32, 22]-code) | [i] | ✔ | |
| 18 | Linear OA(4938, 67, F49, 30) (dual of [67, 29, 31]-code) | [i] | ✔ | |
| 19 | Linear OA(4929, 67, F49, 21) (dual of [67, 38, 22]-code) | [i] | ✔ | |
| 20 | Linear OA(4950, 79, F49, 36) (dual of [79, 29, 37]-code) | [i] | ✔ | |
| 21 | Linear OA(4930, 59, F49, 26) (dual of [59, 29, 27]-code) | [i] | ✔ | |
| 22 | Linear OA(4925, 59, F49, 21) (dual of [59, 34, 22]-code) | [i] | ✔ | |