MinT - Information on Result #899530

Information on Result #899530

Linear OOA(25⁵⁷, 195345, F₂₅, 2, 13) (dual of [(195345, 2), 390633, 14]-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(25⁵¹, 195319, F₂₅, 2, 13) (dual of [(195319, 2), 390587, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁵¹, 390638, F₂₅, 13) (dual of [390638, 390587, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(25⁵¹, 390639, F₂₅, 13) (dual of [390639, 390588, 14]-code), using
    - constructionÂ X applied to C_e(12) âŠ‚ C_e(9) [i] based on
      1. linear OA(25⁴⁹, 390625, F₂₅, 13) (dual of [390625, 390576, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      2. linear OA(25³⁷, 390625, F₂₅, 10) (dual of [390625, 390588, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [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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