MinT - Information on Result #899487

Information on Result #899487

Linear OOA(25⁵³, 195345, F₂₅, 2, 12) (dual of [(195345, 2), 390637, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(25⁶, 26, F₂₅, 2, 6) (dual of [(26, 2), 46, 7]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;46,25) [i]
linear OOA(25⁴⁷, 195319, F₂₅, 2, 12) (dual of [(195319, 2), 390591, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁴⁷, 390638, F₂₅, 12) (dual of [390638, 390591, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(25⁴⁷, 390639, F₂₅, 12) (dual of [390639, 390592, 13]-code), using
    - constructionÂ X applied to C_e(11) âŠ‚ C_e(8) [i] based on
      1. 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]
      2. linear OA(25³³, 390625, F₂₅, 9) (dual of [390625, 390592, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [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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