Information on Result #1720423
Linear OOA(4183, 2740, F4, 39, 32) (dual of [(2740, 39), 106677, 33]-NRT-code), using OOA 6-folding and stacking with additional row based on linear OOA(4183, 16441, F4, 3, 32) (dual of [(16441, 3), 49140, 33]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4183, 16442, F4, 3, 32) (dual of [(16442, 3), 49143, 33]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4183, 16442, F4, 32) (dual of [16442, 16259, 33]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4182, 16440, F4, 32) (dual of [16440, 16258, 33]-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(413, 55, F4, 6) (dual of [55, 42, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- construction X applied to C([0,16]) ⊂ C([0,12]) [i] based on
- linear OA(4182, 16441, F4, 31) (dual of [16441, 16259, 32]-code), using Gilbert–Varšamov bound and bm = 4182 > Vbs−1(k−1) = 2 268811 558949 293422 422571 069668 397283 457733 507637 923233 673591 835947 164213 946139 959695 019896 441186 152573 689004 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 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(4182, 16440, F4, 32) (dual of [16440, 16258, 33]-code), using
- construction X with Varšamov bound [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4183, 16442, F4, 32) (dual of [16442, 16259, 33]-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 (151, 183, 2740)-net over F4 | [i] | Net Defined by OOA | |