Information on Result #682817
Linear OA(5103, 15651, F5, 21) (dual of [15651, 15548, 22]-code), using construction XX applied to Ce(20) ⊂ Ce(16) ⊂ Ce(15) based on
- linear OA(597, 15625, F5, 21) (dual of [15625, 15528, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(579, 15625, F5, 17) (dual of [15625, 15546, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(573, 15625, F5, 16) (dual of [15625, 15552, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(54, 24, F5, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,5)), using
- linear OA(50, 2, F5, 0) (dual of [2, 2, 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: 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 OOA(5103, 11195, F5, 2, 21) (dual of [(11195, 2), 22287, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5103, 11195, F5, 3, 21) (dual of [(11195, 3), 33482, 22]-NRT-code) | [i] | ||
| 3 | Digital (82, 103, 11195)-net over F5 | [i] | ||
| 4 | Linear OOA(5103, 1565, F5, 21, 21) (dual of [(1565, 21), 32762, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |