MinT - Information on Result #836341

Information on Result #836341

Linear OOA(5¹³¹, 195337, F₅, 2, 19) (dual of [(195337, 2), 390543, 20]-NRT-code), using OOA 2-folding based on linear OA(5¹³¹, 390674, F₅, 19) (dual of [390674, 390543, 20]-code), using

discarding factors / shortening the dual code based on linear OA(5¹³¹, 390675, F₅, 19) (dual of [390675, 390544, 20]-code), using
- constructionÂ X applied to C_e(18) âŠ‚ C_e(12) [i] based on
  1. linear OA(5¹²¹, 390625, F₅, 19) (dual of [390625, 390504, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 5⁸âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
  2. linear OA(5⁸¹, 390625, F₅, 13) (dual of [390625, 390544, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 5⁸âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
  3. linear OA(5¹⁰, 50, F₅, 5) (dual of [50, 40, 6]-code), using
    - discarding factors / shortening the dual code based on linear OA(5¹⁰, 52, F₅, 5) (dual of [52, 42, 6]-code), using
      - trace code [i] based on linear OA(25⁵, 26, F₂₅, 5) (dual of [26, 21, 6]-code or 26-arc in PG(4,25)), using
        extended Reedâ€“Solomon code RS_e(21,25) [i]
        the expurgated narrow-sense BCH-code C(I) with length 26Â | 25²âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
        algebraic-geometric code AG(F,10P) with 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, Q+6P) with degQ = 2 and degPÂ =Â 3 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26 (see above)

Mode: Constructive and 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.