Information on Result #1731284
Digital (37, 51, 2082)-net over F9, using net defined by OOA based on linear OOA(951, 2082, F9, 21, 14) (dual of [(2082, 21), 43671, 15]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(951, 6247, F9, 3, 14) (dual of [(6247, 3), 18690, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(951, 6249, F9, 3, 14) (dual of [(6249, 3), 18696, 15]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(951, 6249, F9, 14) (dual of [6249, 6198, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(951, 6572, F9, 14) (dual of [6572, 6521, 15]-code), using
- construction XX applied to Ce(13) ⊂ Ce(11) ⊂ Ce(10) [i] based on
- linear OA(949, 6561, F9, 14) (dual of [6561, 6512, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(941, 6561, F9, 12) (dual of [6561, 6520, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(937, 6561, F9, 11) (dual of [6561, 6524, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(91, 10, F9, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, 728, F9, 1) (dual of [728, 727, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(91, 728, F9, 1) (dual of [728, 727, 2]-code), using
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(13) ⊂ Ce(11) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(951, 6572, F9, 14) (dual of [6572, 6521, 15]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(951, 6249, F9, 14) (dual of [6249, 6198, 15]-code), using
- discarding factors / shortening the dual code based on linear OOA(951, 6249, F9, 3, 14) (dual of [(6249, 3), 18696, 15]-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, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.