Information on Result #1720563
Linear OOA(4187, 2741, F4, 39, 33) (dual of [(2741, 39), 106712, 34]-NRT-code), using OOA 6-folding and stacking with additional row based on linear OOA(4187, 16447, F4, 3, 33) (dual of [(16447, 3), 49154, 34]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4187, 16448, F4, 3, 33) (dual of [(16448, 3), 49157, 34]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4187, 16448, F4, 33) (dual of [16448, 16261, 34]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4183, 16441, F4, 33) (dual of [16441, 16258, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,12]) [i] based on
- linear OA(4169, 16385, F4, 33) (dual of [16385, 16216, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(4127, 16385, F4, 25) (dual of [16385, 16258, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(414, 56, F4, 7) (dual of [56, 42, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- a “GraXX†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- construction X applied to C([0,16]) ⊂ C([0,12]) [i] based on
- linear OA(4183, 16444, F4, 31) (dual of [16444, 16261, 32]-code), using Gilbert–Varšamov bound and bm = 4183 > Vbs−1(k−1) = 2 281275 752639 839628 473199 693768 989594 550212 751797 287055 435974 830411 787802 510662 529396 886697 416272 676866 116904 [i]
- linear OA(41, 4, F4, 1) (dual of [4, 3, 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
- linear OA(4183, 16441, F4, 33) (dual of [16441, 16258, 34]-code), using
- construction X with Varšamov bound [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4187, 16448, F4, 33) (dual of [16448, 16261, 34]-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 (154, 187, 2741)-net over F4 | [i] | Net Defined by OOA | |