Information on Result #1718471
Linear OOA(4122, 15375, F4, 21, 19) (dual of [(15375, 21), 322753, 20]-NRT-code), using OOA 3-folding and stacking with additional row based on linear OOA(4122, 46126, F4, 3, 19) (dual of [(46126, 3), 138256, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4122, 46127, F4, 3, 19) (dual of [(46127, 3), 138259, 20]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4122, 46127, F4, 19) (dual of [46127, 46005, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(4122, 65563, F4, 19) (dual of [65563, 65441, 20]-code), using
- construction XX applied to C1 = C([0,8]), C2 = C([1,9]), C3 = C1 + C2 = C([1,8]), and C∩ = C1 ∩ C2 = C([0,9]) [i] based on
- linear OA(497, 65537, F4, 17) (dual of [65537, 65440, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(4112, 65537, F4, 10) (dual of [65537, 65425, 11]-code), using the narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [1,9], and minimum distance d ≥ |{−9,−7,−5,…,9}|+1 = 11 (BCH-bound) [i]
- linear OA(4113, 65537, F4, 19) (dual of [65537, 65424, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(496, 65537, F4, 8) (dual of [65537, 65441, 9]-code), using the narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(48, 9, F4, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,4)), using
- dual of repetition code with length 9 [i]
- linear OA(41, 17, F4, 1) (dual of [17, 16, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction XX applied to C1 = C([0,8]), C2 = C([1,9]), C3 = C1 + C2 = C([1,8]), and C∩ = C1 ∩ C2 = C([0,9]) [i] based on
- discarding factors / shortening the dual code based on linear OA(4122, 65563, F4, 19) (dual of [65563, 65441, 20]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4122, 46127, F4, 19) (dual of [46127, 46005, 20]-code), using
Mode: Linear.
Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (103, 122, 15375)-net over F4 | [i] | Net Defined by OOA | |