Information on Result #1454504
Linear OOA(16101, 1048602, F16, 2, 21) (dual of [(1048602, 2), 2097103, 22]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(16101, 1048602, F16, 21) (dual of [1048602, 1048501, 22]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(16100, 1048600, F16, 21) (dual of [1048600, 1048500, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- linear OA(1696, 1048576, F16, 21) (dual of [1048576, 1048480, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(1676, 1048576, F16, 17) (dual of [1048576, 1048500, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(164, 24, F16, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,16)), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- linear OA(16100, 1048601, F16, 20) (dual of [1048601, 1048501, 21]-code), using Gilbert–Varšamov bound and bm = 16100 > Vbs−1(k−1) = 448906 833831 178424 584602 865044 127760 714759 632923 197901 495524 020849 976151 726418 898937 751398 474126 221749 399376 415357 249001 [i]
- linear OA(160, 1, F16, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(16100, 1048600, F16, 21) (dual of [1048600, 1048500, 22]-code), 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(16101, 209720, F16, 22, 21) (dual of [(209720, 22), 4613739, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |