MinT - Information on Result #2504394

Information on Result #2504394

Linear OOA(5¹¹¹, 1587, F₅, 2, 24) (dual of [(1587, 2), 3063, 25]-NRT-code), using 5¹ times duplication based on linear OOA(5¹¹⁰, 1587, F₅, 2, 24) (dual of [(1587, 2), 3064, 25]-NRT-code), using

OOA 2-folding [i] based on linear OA(5¹¹⁰, 3174, F₅, 24) (dual of [3174, 3064, 25]-code), using
- constructionÂ X applied to C_e(23) âŠ‚ C_e(15) [i] based on
  1. linear OA(5⁹⁶, 3125, F₅, 24) (dual of [3125, 3029, 25]-code), using an extension C_e(23) of the primitive narrow-sense BCH-code C(I) with length 3124Â = 5⁵âˆ’1, defining interval IÂ =Â [1,23], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]
  2. linear OA(5⁶¹, 3125, F₅, 16) (dual of [3125, 3064, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 3124Â = 5⁵âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
  3. linear OA(5¹⁴, 49, F₅, 7) (dual of [49, 35, 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.