MinT - Information on Result #1300162

Information on Result #1300162

Linear OA(4¹²⁸, 157, F₄, 68) (dual of [157, 29, 69]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(4¹²⁷, 155, F₄, 68) (dual of [155, 28, 69]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(4¹²⁶, 153, F₄, 68) (dual of [153, 27, 69]-code), using
    - 3 times truncation [i] based on linear OA(4¹²⁹, 156, F₄, 71) (dual of [156, 27, 72]-code), using
      - concatenation of two codes [i] based on
        linear OA(64¹⁷, 26, F₆₄, 17) (dual of [26, 9, 18]-code or 26-arc in PG(16,64)), using
        discarding factors / shortening the dual code based on linear OA(64¹⁷, 64, F₆₄, 17) (dual of [64, 47, 18]-code or 64-arc in PG(16,64)), using
        Reedâ€“Solomon code RS(47,64) [i]
        linear OA(4³, 6, F₄, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,4) or 6-cap in PG(2,4)), using
        hyperoval in PG(2,Â 4) [i]
        the Hexacode [i]
  2. linear OA(4¹²⁶, 154, F₄, 67) (dual of [154, 28, 68]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4¹²⁶Â > V_b^sâˆ’1(kâˆ’1)Â = 7184 975838 402336 137119 320135 915249 664166 649865 634788 842484 923377 838120 409936 [i]
  3. linear OA(4⁰, 1, F₄, 0) (dual of [1, 1, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(4⁰, s, F₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
      - OA with only one run / dual of code without redundancy [i]
linear OA(4¹²⁷, 156, F₄, 67) (dual of [156, 29, 68]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4¹²⁷Â > V_b^sâˆ’1(kâˆ’1)Â = 21741 030504 282348 810972 238281 573953 191728 794268 536057 702801 145006 301178 208526 [i]
linear OA(4⁰, 1, F₄, 0) (dual of [1, 1, 1]-code) (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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

None.