Information on Result #1445369
Linear OOA(8115, 262177, F8, 2, 21) (dual of [(262177, 2), 524239, 22]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(8115, 262177, F8, 21) (dual of [262177, 262062, 22]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8113, 262173, F8, 21) (dual of [262173, 262060, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(8109, 262145, F8, 21) (dual of [262145, 262036, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 812−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(885, 262145, F8, 17) (dual of [262145, 262060, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 812−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(84, 28, F8, 3) (dual of [28, 24, 4]-code or 28-cap in PG(3,8)), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(8113, 262175, F8, 20) (dual of [262175, 262062, 21]-code), using Gilbert–Varšamov bound and bm = 8113 > Vbs−1(k−1) = 840798 926494 272918 715549 677710 017530 374324 813929 507153 650096 768776 720969 414464 922715 674865 685521 940390 [i]
- linear OA(80, 2, F8, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(8113, 262173, F8, 21) (dual of [262173, 262060, 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(8115, 131088, F8, 3, 21) (dual of [(131088, 3), 393149, 22]-NRT-code) | [i] | OOA Folding | |