MinT - Information on Result #1300203

Information on Result #1300203

Linear OA(4¹³⁷, 169, F₄, 72) (dual of [169, 32, 73]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(4¹³⁶, 167, F₄, 72) (dual of [167, 31, 73]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(4¹³⁵, 165, F₄, 72) (dual of [165, 30, 73]-code), using
    - 3 times truncation [i] based on linear OA(4¹³⁸, 168, F₄, 75) (dual of [168, 30, 76]-code), using
      - concatenation of two codes [i] based on
        linear OA(64¹⁸, 28, F₆₄, 18) (dual of [28, 10, 19]-code or 28-arc in PG(17,64)), using
        discarding factors / shortening the dual code based on linear OA(64¹⁸, 64, F₆₄, 18) (dual of [64, 46, 19]-code or 64-arc in PG(17,64)), using
        Reedâ€“Solomon code RS(46,64) [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(4¹³⁵, 166, F₄, 71) (dual of [166, 31, 72]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4¹³⁵Â > V_b^sâˆ’1(kâˆ’1)Â = 1445 994932 487951 446371 309153 545159 071816 579369 357390 566819 026250 267201 823859 878176 [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(4¹³⁶, 168, F₄, 71) (dual of [168, 32, 72]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4¹³⁶Â > V_b^sâˆ’1(kâˆ’1)Â = 4277 355062 933776 371704 583614 881565 920038 155264 975599 798495 941270 628041 300886 537066 [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.