MinT - Information on Result #973522

Information on Result #973522

Linear OOA(5¹³⁵, 1056, F₅, 3, 31) (dual of [(1056, 3), 3033, 32]-NRT-code), using OOA 3-folding based on linear OA(5¹³⁵, 3168, F₅, 31) (dual of [3168, 3033, 32]-code), using

discarding factors / shortening the dual code based on linear OA(5¹³⁵, 3170, F₅, 31) (dual of [3170, 3035, 32]-code), using
- constructionÂ X applied to C([0,15]) âŠ‚ C([0,11]) [i] based on
  1. linear OA(5¹²¹, 3126, F₅, 31) (dual of [3126, 3005, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 3126Â | 5¹⁰âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (BCH-bound) [i]
  2. linear OA(5⁹¹, 3126, F₅, 23) (dual of [3126, 3035, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 3126Â | 5¹⁰âˆ’1, defining interval IÂ =Â [0,11], and minimum distance dÂ â‰¥ |{−11,−10,…,11}|+1Â =Â 24 (BCH-bound) [i]
  3. linear OA(5¹⁴, 44, F₅, 7) (dual of [44, 30, 8]-code), using
    - discarding factors / shortening the dual code based on linear OA(5¹⁴, 52, F₅, 7) (dual of [52, 38, 8]-code), using
      - trace code [i] based on linear OA(25⁷, 26, F₂₅, 7) (dual of [26, 19, 8]-code or 26-arc in PG(6,25)), using
        extended Reedâ€“Solomon code RS_e(19,25) [i]
        the expurgated narrow-sense BCH-code C(I) with length 26Â | 25²âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
        algebraic-geometric code AG(F,9P) 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,6P) with 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.