MinT - Information on Result #904102

Information on Result #904102

Linear OOA(64⁸⁴, 2230, F₆₄, 2, 30) (dual of [(2230, 2), 4376, 31]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64²², 177, F₆₄, 2, 15) (dual of [(177, 2), 332, 16]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,338P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
  - a function field by GarcÃa and Quoos [i]
linear OOA(64⁶², 2053, F₆₄, 2, 30) (dual of [(2053, 2), 4044, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(64⁶², 4106, F₆₄, 30) (dual of [4106, 4044, 31]-code), using
  - discarding factors / shortening the dual code based on linear OA(64⁶², 4107, F₆₄, 30) (dual of [4107, 4045, 31]-code), using
    - constructionÂ X applied to C_e(29) âŠ‚ C_e(25) [i] based on
      1. linear OA(64⁵⁹, 4096, F₆₄, 30) (dual of [4096, 4037, 31]-code), using an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
      2. linear OA(64⁵¹, 4096, F₆₄, 26) (dual of [4096, 4045, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
      3. linear OA(64³, 11, F₆₄, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,64) or 11-cap in PG(2,64)), using
        discarding factors / shortening the dual code based on linear OA(64³, 64, F₆₄, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
        Reedâ€“Solomon code RS(61,64) [i]

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.