MinT - Information on Result #1196629

Information on Result #1196629

Linear OOA(25⁷⁵, 43406, F₂₅, 18, 18) (dual of [(43406, 18), 781233, 19]-NRT-code), using OA 9-folding and stacking based on linear OA(25⁷⁵, 390654, F₂₅, 18) (dual of [390654, 390579, 19]-code), using

constructionÂ X applied to C_e(17) âŠ‚ C_e(11) [i] based on
1. linear OA(25⁶⁹, 390625, F₂₅, 18) (dual of [390625, 390556, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
2. linear OA(25⁴⁵, 390625, F₂₅, 12) (dual of [390625, 390580, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
3. linear OA(25⁶, 29, F₂₅, 5) (dual of [29, 23, 6]-code), using
  - construction for [s,Â sâˆ’6,Â 6]-code from [s,Â 3,Â sâˆ’3]-code [i] based on linear OA(25²⁶, 29, F₂₅, 25) (dual of [29, 3, 26]-code), using
    - constructionÂ X applied to C₁ âŠ‚ C₀ [i] based on
      1. linear OA(25²⁵, 26, F₂₅, 25) (dual of [26, 1, 26]-code or 26-arc in PG(24,25)), using code C₁ for uÂ =Â 2 by de Boer and Brouwer [i]
      2. linear OA(25²³, 26, F₂₅, 23) (dual of [26, 3, 24]-code or 26-arc in PG(22,25)), using code C₀ for uÂ =Â 2 by de Boer and Brouwer [i]
      3. linear OA(25¹, 3, F₂₅, 1) (dual of [3, 2, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(25¹, s, F₂₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]

Mode: Constructive and 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 (57, 75, 43406)-net over F₂₅	[i]		Net Defined by OOA