MinT - Information on Result #1480246

Information on Result #1480246

Linear OOA(4¹⁷⁹, 2120, F₄, 3, 38) (dual of [(2120, 3), 6181, 39]-NRT-code), using OOA 2-folding based on linear OOA(4¹⁷⁹, 4240, F₄, 2, 38) (dual of [(4240, 2), 8301, 39]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4¹⁷⁹, 4241, F₄, 2, 38) (dual of [(4241, 2), 8303, 39]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(4¹⁷⁹, 4241, F₄, 38) (dual of [4241, 4062, 39]-code), using
  - 129 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (3, 1, 0, 1, 4 times 0, 1, 7 times 0, 1, 12 times 0, 1, 19 times 0, 1, 31 times 0, 1, 47 times 0) [i] based on linear OA(4¹⁶⁹, 4102, F₄, 38) (dual of [4102, 3933, 39]-code), using
    - constructionÂ X applied to C_e(37) âŠ‚ C_e(36) [i] based on
      1. linear OA(4¹⁶⁹, 4096, F₄, 38) (dual of [4096, 3927, 39]-code), using an extension C_e(37) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 4⁶âˆ’1, defining interval IÂ =Â [1,37], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 38 [i]
      2. linear OA(4¹⁶³, 4096, F₄, 37) (dual of [4096, 3933, 38]-code), using an extension C_e(36) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 4⁶âˆ’1, defining interval IÂ =Â [1,36], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 37 [i]
      3. linear OA(4⁰, 6, F₄, 0) (dual of [6, 6, 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]

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.