MinT - Information on Result #1301870

Information on Result #1301870

Linear OA(5¹³⁸, 157, F₅, 86) (dual of [157, 19, 87]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(5¹³⁵, 153, F₅, 86) (dual of [153, 18, 87]-code), using
- 3 times truncation [i] based on linear OA(5¹³⁸, 156, F₅, 89) (dual of [156, 18, 90]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(25¹⁷, 26, F₂₅, 17) (dual of [26, 9, 18]-code or 26-arc in PG(16,25)), using
      - extended Reedâ€“Solomon code RS_e(9,25) [i]
      - the expurgated narrow-sense BCH-code C(I) with length 26Â | 25²âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
      - algebraic-geometric code AG(F,4P) 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+2P) with degQ = 2 and degPÂ =Â 3 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26 (see above)
    2. linear OA(5⁴, 6, F₅, 4) (dual of [6, 2, 5]-code or 6-arc in PG(3,5)), using
      - extended Reedâ€“Solomon code RS_e(2,5) [i]
      - Simplex code S(2,5) [i]
linear OA(5¹³⁵, 154, F₅, 83) (dual of [154, 19, 84]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 5¹³⁵Â > V_b^sâˆ’1(kâˆ’1)Â = 16160 601135 038304 327854 023004 003446 033546 248413 441600 036635 336244 724280 448730 230083 065536 485925 [i]
linear OA(5², 3, F₅, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,5)), using
- dual of repetition code with length 3 [i]

Mode: Linear.

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None.