MinT - Information on Result #1495251

Information on Result #1495251

Linear OOA(64⁸³, 2264, F₆₄, 3, 36) (dual of [(2264, 3), 6709, 37]-NRT-code), using OOA 2-folding based on linear OOA(64⁸³, 4528, F₆₄, 2, 36) (dual of [(4528, 2), 8973, 37]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(64⁸³, 4529, F₆₄, 2, 36) (dual of [(4529, 2), 8975, 37]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(64⁸³, 4529, F₆₄, 36) (dual of [4529, 4446, 37]-code), using
  - 419 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (6, 0, 0, 1, 4 times 0, 1, 13 times 0, 1, 26 times 0, 1, 55 times 0, 1, 108 times 0, 1, 204 times 0) [i] based on linear OA(64⁷¹, 4098, F₆₄, 36) (dual of [4098, 4027, 37]-code), using
    - constructionÂ X applied to C_e(35) âŠ‚ C_e(34) [i] based on
      1. linear OA(64⁷¹, 4096, F₆₄, 36) (dual of [4096, 4025, 37]-code), using an extension C_e(35) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,35], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 36 [i]
      2. linear OA(64⁶⁹, 4096, F₆₄, 35) (dual of [4096, 4027, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
      3. linear OA(64⁰, 2, F₆₄, 0) (dual of [2, 2, 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: 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.