MinT - Information on Result #899624

Information on Result #899624

Linear OOA(25⁶⁶, 195345, F₂₅, 2, 15) (dual of [(195345, 2), 390624, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(25⁷, 26, F₂₅, 2, 7) (dual of [(26, 2), 45, 8]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;45,25) [i]
linear OOA(25⁵⁹, 195319, F₂₅, 2, 15) (dual of [(195319, 2), 390579, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁵⁹, 390638, F₂₅, 15) (dual of [390638, 390579, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(25⁵⁹, 390639, F₂₅, 15) (dual of [390639, 390580, 16]-code), using
    - constructionÂ X applied to C_e(14) âŠ‚ C_e(11) [i] based on
      1. linear OA(25⁵⁷, 390625, F₂₅, 15) (dual of [390625, 390568, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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(25², 14, F₂₅, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,25)), using
        discarding factors / shortening the dual code based on linear OA(25², 25, F₂₅, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
        Reedâ€“Solomon code RS(23,25) [i]

Mode: Constructive and linear.

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