Information on Result #1556962
Linear OOA(8136, 2097198, F8, 3, 21) (dual of [(2097198, 3), 6291458, 22]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(8136, 2097198, F8, 21) (dual of [2097198, 2097062, 22]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8134, 2097194, F8, 21) (dual of [2097194, 2097060, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(14) [i] based on
- linear OA(8127, 2097152, F8, 21) (dual of [2097152, 2097025, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(892, 2097152, F8, 15) (dual of [2097152, 2097060, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(87, 42, F8, 5) (dual of [42, 35, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- construction X applied to Ce(20) ⊂ Ce(14) [i] based on
- linear OA(8134, 2097196, F8, 20) (dual of [2097196, 2097062, 21]-code), using Gilbert–Varšamov bound and bm = 8134 > Vbs−1(k−1) = 121023 789833 573070 970547 361235 879171 146413 601828 082133 331751 289792 497413 050816 988363 889283 307045 254084 047894 790012 617840 [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(8134, 2097194, F8, 21) (dual of [2097194, 2097060, 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(8136, 524299, F8, 27, 21) (dual of [(524299, 27), 14155937, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |