Information on Result #1324300
Linear OA(5127, 78183, F5, 21) (dual of [78183, 78056, 22]-code), using construction X with Varšamov bound based on
- linear OA(5126, 78181, F5, 21) (dual of [78181, 78055, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,6]) [i] based on
- linear OA(5113, 78126, F5, 21) (dual of [78126, 78013, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(571, 78126, F5, 13) (dual of [78126, 78055, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(513, 55, F5, 7) (dual of [55, 42, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(513, 63, F5, 7) (dual of [63, 50, 8]-code), using
- a “GraCyc†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(513, 63, F5, 7) (dual of [63, 50, 8]-code), using
- construction X applied to C([0,10]) ⊂ C([0,6]) [i] based on
- linear OA(5126, 78182, F5, 20) (dual of [78182, 78056, 21]-code), using Gilbert–Varšamov bound and bm = 5126 > Vbs−1(k−1) = 2099 156559 884603 461655 092345 832478 775579 268574 640445 534313 971323 535283 809699 742258 591925 [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(5127, 78183, F5, 2, 21) (dual of [(78183, 2), 156239, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5127, 78183, F5, 3, 21) (dual of [(78183, 3), 234422, 22]-NRT-code) | [i] | ||
| 3 | Digital (106, 127, 78183)-net over F5 | [i] | ||
| 4 | Linear OOA(5127, 39091, F5, 2, 21) (dual of [(39091, 2), 78055, 22]-NRT-code) | [i] | OOA Folding | |