MinT - Information on Result #873838

Information on Result #873838

Linear OOA(64⁴⁰, 133122, F₆₄, 2, 11) (dual of [(133122, 2), 266204, 12]-NRT-code), using OOA 2-folding based on linear OA(64⁴⁰, 266244, F₆₄, 11) (dual of [266244, 266204, 12]-code), using

discarding factors / shortening the dual code based on linear OA(64⁴⁰, 266245, F₆₄, 11) (dual of [266245, 266205, 12]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(64⁹, 4098, F₆₄, 5) (dual of [4098, 4089, 6]-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OA(64², 65, F₆₄, 2) (dual of [65, 63, 3]-code or 65-arc in PG(1,64)), using
        extended Reedâ€“Solomon code RS_e(63,64) [i]
        Hamming code H(2,64) [i]
      2. linear OA(64⁷, 4033, F₆₄, 5) (dual of [4033, 4026, 6]-code), using
        a code by Danev and Olsson [i]
  2. linear OA(64³¹, 262147, F₆₄, 11) (dual of [262147, 262116, 12]-code), using
    - constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
      1. linear OA(64³¹, 262144, F₆₄, 11) (dual of [262144, 262113, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      2. linear OA(64²⁸, 262144, F₆₄, 10) (dual of [262144, 262116, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
      3. linear OA(64⁰, 3, F₆₄, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(64⁰, s, F₆₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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.