Information on Result #1613091
Linear OOA(3249, 4194484, F3, 4, 22) (dual of [(4194484, 4), 16777687, 23]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3249, 4194484, F3, 2, 22) (dual of [(4194484, 2), 8388719, 23]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(338, 183, F3, 2, 11) (dual of [(183, 2), 328, 12]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(338, 183, F3, 11) (dual of [183, 145, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(338, 251, F3, 11) (dual of [251, 213, 12]-code), using
- construction XX applied to Ce(10) ⊂ Ce(9) ⊂ Ce(7) [i] based on
- linear OA(336, 243, F3, 11) (dual of [243, 207, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(331, 243, F3, 10) (dual of [243, 212, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(326, 243, F3, 8) (dual of [243, 217, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(30, 6, F3, 0) (dual of [6, 6, 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
- linear OA(31, 2, F3, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(10) ⊂ Ce(9) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(338, 251, F3, 11) (dual of [251, 213, 12]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(338, 183, F3, 11) (dual of [183, 145, 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(338, 183, F3, 2, 11) (dual of [(183, 2), 328, 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(3249, 1398161, F3, 28, 22) (dual of [(1398161, 28), 39148259, 23]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |