MinT - Information on Result #1485287

Information on Result #1485287

Linear OOA(5¹⁴⁴, 679865, F₅, 3, 19) (dual of [(679865, 3), 2039451, 20]-NRT-code), using OOA 2-folding based on linear OOA(5¹⁴⁴, 1359730, F₅, 2, 19) (dual of [(1359730, 2), 2719316, 20]-NRT-code), using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(5¹⁴⁴, 1359730, F₅, 19) (dual of [1359730, 1359586, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(5¹⁴⁴, 1953169, F₅, 19) (dual of [1953169, 1953025, 20]-code), using
  - constructionÂ X applied to C_e(18) âŠ‚ C_e(13) [i] based on
    1. linear OA(5¹³⁶, 1953125, F₅, 19) (dual of [1953125, 1952989, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 1953124Â = 5⁹âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    2. linear OA(5¹⁰⁰, 1953125, F₅, 14) (dual of [1953125, 1953025, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 1953124Â = 5⁹âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
    3. linear OA(5⁸, 44, F₅, 4) (dual of [44, 36, 5]-code), using
      - discarding factors / shortening the dual code based on linear OA(5⁸, 52, F₅, 4) (dual of [52, 44, 5]-code), using
        trace code [i] based on linear OA(25⁴, 26, F₂₅, 4) (dual of [26, 22, 5]-code or 26-arc in PG(3,25)), using
        extended Reedâ€“Solomon code RS_e(22,25) [i]
        algebraic-geometric code AG(F, Q+9P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using the rational function field F₂₅(x) [i]
        algebraic-geometric code AG(F,7P) with degPÂ =Â 3 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26 (see above)

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.