Information on Result #1612794
Linear OOA(3246, 4194426, F3, 4, 22) (dual of [(4194426, 4), 16777458, 23]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3246, 4194426, F3, 2, 22) (dual of [(4194426, 2), 8388606, 23]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(335, 125, F3, 2, 11) (dual of [(125, 2), 215, 12]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(335, 125, F3, 11) (dual of [125, 90, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(335, 126, F3, 11) (dual of [126, 91, 12]-code), using
- construction X applied to C({2,4,7,11,13,17,25}) ⊂ C({2,4,7,11,17,25}) [i] based on
- linear OA(335, 121, F3, 11) (dual of [121, 86, 12]-code), using the cyclic code C(A) with length 121 | 35−1, defining set A = {2,4,7,11,13,17,25}, and minimum distance d ≥ |{13,32,51,…,−39}|+1 = 12 (BCH-bound) [i]
- linear OA(330, 121, F3, 10) (dual of [121, 91, 11]-code), using the cyclic code C(A) with length 121 | 35−1, defining set A = {2,4,7,11,17,25}, and minimum distance d ≥ |{32,51,70,…,−39}|+1 = 11 (BCH-bound) [i]
- linear OA(30, 5, F3, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to C({2,4,7,11,13,17,25}) ⊂ C({2,4,7,11,17,25}) [i] based on
- discarding factors / shortening the dual code based on linear OA(335, 126, F3, 11) (dual of [126, 91, 12]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(335, 125, F3, 11) (dual of [125, 90, 12]-code), using
- linear OOA(3211, 4194301, F3, 2, 22) (dual of [(4194301, 2), 8388391, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3211, 8388602, F3, 22) (dual of [8388602, 8388391, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3211, large, F3, 22) (dual of [large, large−211, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(3211, large, F3, 22) (dual of [large, large−211, 23]-code), using
- OOA 2-folding [i] based on linear OA(3211, 8388602, F3, 22) (dual of [8388602, 8388391, 23]-code), using
- linear OOA(335, 125, F3, 2, 11) (dual of [(125, 2), 215, 12]-NRT-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(3246, 1398141, F3, 28, 22) (dual of [(1398141, 28), 39147702, 23]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |