Information on Result #1443955
Linear OOA(875, 2097178, F8, 2, 12) (dual of [(2097178, 2), 4194281, 13]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(875, 2097178, F8, 12) (dual of [2097178, 2097103, 13]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(874, 2097176, F8, 12) (dual of [2097176, 2097102, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- linear OA(871, 2097152, F8, 12) (dual of [2097152, 2097081, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(850, 2097152, F8, 9) (dual of [2097152, 2097102, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(83, 24, F8, 2) (dual of [24, 21, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- linear OA(874, 2097177, F8, 11) (dual of [2097177, 2097103, 12]-code), using Gilbert–Varšamov bound and bm = 874 > Vbs−1(k−1) = 128102 361101 264540 908329 698815 640863 772881 568097 645042 242732 791298 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 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(874, 2097176, F8, 12) (dual of [2097176, 2097102, 13]-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(875, 1048589, F8, 3, 12) (dual of [(1048589, 3), 3145692, 13]-NRT-code) | [i] | OOA Folding | |