MinT - Information on Result #1300256

Information on Result #1300256

Linear OA(4¹⁴², 177, F₄, 74) (dual of [177, 35, 75]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(4¹⁴¹, 175, F₄, 74) (dual of [175, 34, 75]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(4¹⁴⁰, 173, F₄, 74) (dual of [173, 33, 75]-code), using
    - 1 times truncation [i] based on linear OA(4¹⁴¹, 174, F₄, 75) (dual of [174, 33, 76]-code), using
      - concatenation of two codes [i] based on
        linear OA(64¹⁸, 29, F₆₄, 18) (dual of [29, 11, 19]-code or 29-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(4¹⁴⁰, 174, F₄, 73) (dual of [174, 34, 74]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4¹⁴⁰Â > V_b^sâˆ’1(kâˆ’1)Â = 1 880731 159670 590432 006388 875508 944671 132309 303015 490192 382398 439062 326235 660138 491766 [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(4¹⁴¹, 176, F₄, 73) (dual of [176, 35, 74]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4¹⁴¹Â > V_b^sâˆ’1(kâˆ’1)Â = 5 419596 469169 437254 012019 831414 512702 006274 974452 858721 374951 719937 390579 968951 230046 [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.