Information on Result #895608
Linear OOA(4176, 4194817, F4, 2, 17) (dual of [(4194817, 2), 8389458, 18]-NRT-code), using (u, u+v)-construction based on
- linear OOA(431, 516, F4, 2, 8) (dual of [(516, 2), 1001, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(431, 1032, F4, 8) (dual of [1032, 1001, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(431, 1033, F4, 8) (dual of [1033, 1002, 9]-code), using
- construction XX applied to C1 = C([1022,5]), C2 = C([0,6]), C3 = C1 + C2 = C([0,5]), and C∩ = C1 ∩ C2 = C([1022,6]) [i] based on
- linear OA(426, 1023, F4, 7) (dual of [1023, 997, 8]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−1,0,…,5}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(426, 1023, F4, 7) (dual of [1023, 997, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(431, 1023, F4, 8) (dual of [1023, 992, 9]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−1,0,…,6}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(421, 1023, F4, 6) (dual of [1023, 1002, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(40, 5, F4, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(40, 5, F4, 0) (dual of [5, 5, 1]-code) (see above)
- construction XX applied to C1 = C([1022,5]), C2 = C([0,6]), C3 = C1 + C2 = C([0,5]), and C∩ = C1 ∩ C2 = C([1022,6]) [i] based on
- discarding factors / shortening the dual code based on linear OA(431, 1033, F4, 8) (dual of [1033, 1002, 9]-code), using
- OOA 2-folding [i] based on linear OA(431, 1032, F4, 8) (dual of [1032, 1001, 9]-code), using
- linear OOA(4145, 4194301, F4, 2, 17) (dual of [(4194301, 2), 8388457, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4145, 8388602, F4, 17) (dual of [8388602, 8388457, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(4145, large, F4, 17) (dual of [large, large−145, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(4145, large, F4, 17) (dual of [large, large−145, 18]-code), using
- OOA 2-folding [i] based on linear OA(4145, 8388602, F4, 17) (dual of [8388602, 8388457, 18]-code), using
Mode: Constructive and 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(4176, 1048704, F4, 18, 17) (dual of [(1048704, 18), 18876496, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |