Information on Result #638169
Linear OA(5146, 156, F5, 109) (dual of [156, 10, 110]-code), using concatenation of two codes based on
- linear OA(2521, 26, F25, 21) (dual of [26, 5, 22]-code or 26-arc in PG(20,25)), using
- extended Reed–Solomon code RSe(5,25) [i]
- the expurgated narrow-sense BCH-code C(I) with length 26 | 252−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- algebraic-geometric code AG(F,2P) with degPÂ =Â 2 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using the rational function field F25(x) [i]
- algebraic-geometric code AG(F, Q+0P) with degQ = 4 and degPÂ =Â 3 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- linear OA(54, 6, F5, 4) (dual of [6, 2, 5]-code or 6-arc in PG(3,5)), using
- extended Reed–Solomon code RSe(2,5) [i]
- Simplex code S(2,5) [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
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(5146, 156, F5, 108) (dual of [156, 10, 109]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(5146, 156, F5, 107) (dual of [156, 10, 108]-code) | [i] | ||
| 3 | Linear OA(5146, 156, F5, 106) (dual of [156, 10, 107]-code) | [i] | ||
| 4 | Linear OA(5146, 156, F5, 105) (dual of [156, 10, 106]-code) | [i] | ||
| 5 | Linear OA(5147, 157, F5, 109) (dual of [157, 10, 110]-code) | [i] | Code Embedding in Larger Space | |
| 6 | Linear OA(5148, 158, F5, 109) (dual of [158, 10, 110]-code) | [i] | ||
| 7 | Linear OA(5149, 159, F5, 109) (dual of [159, 10, 110]-code) | [i] | ||
| 8 | Linear OA(5150, 160, F5, 109) (dual of [160, 10, 110]-code) | [i] | ||
| 9 | Linear OA(5145, 155, F5, 108) (dual of [155, 10, 109]-code) | [i] | Truncation | |
| 10 | Linear OA(5144, 154, F5, 107) (dual of [154, 10, 108]-code) | [i] | ||
| 11 | Linear OA(5143, 153, F5, 106) (dual of [153, 10, 107]-code) | [i] | ||
| 12 | Linear OA(5142, 152, F5, 105) (dual of [152, 10, 106]-code) | [i] | ||
| 13 | Linear OA(5141, 151, F5, 104) (dual of [151, 10, 105]-code) | [i] | ||
| 14 | Linear OA(5139, 149, F5, 102) (dual of [149, 10, 103]-code) | [i] | ||
| 15 | Linear OA(5138, 148, F5, 101) (dual of [148, 10, 102]-code) | [i] | ||
| 16 | Linear OA(5137, 147, F5, 100) (dual of [147, 10, 101]-code) | [i] | ||
| 17 | Linear OA(5136, 146, F5, 99) (dual of [146, 10, 100]-code) | [i] | ||
| 18 | Linear OA(5135, 145, F5, 98) (dual of [145, 10, 99]-code) | [i] | ||
| 19 | Linear OA(5133, 143, F5, 96) (dual of [143, 10, 97]-code) | [i] | ||
| 20 | Linear OA(5132, 142, F5, 95) (dual of [142, 10, 96]-code) | [i] | ||
| 21 | Linear OA(5131, 141, F5, 94) (dual of [141, 10, 95]-code) | [i] | ||
| 22 | Linear OA(5130, 140, F5, 93) (dual of [140, 10, 94]-code) | [i] | ||
| 23 | Linear OA(5129, 139, F5, 92) (dual of [139, 10, 93]-code) | [i] | ||
| 24 | Linear OA(5127, 137, F5, 90) (dual of [137, 10, 91]-code) | [i] | ||
| 25 | Linear OOA(5146, 78, F5, 2, 109) (dual of [(78, 2), 10, 110]-NRT-code) | [i] | OOA Folding | |
| 26 | Linear OOA(5146, 52, F5, 3, 109) (dual of [(52, 3), 10, 110]-NRT-code) | [i] | ||