MinT - Information on Result #1480427

Information on Result #1480427

Linear OOA(4¹⁸¹, 1765, F₄, 3, 40) (dual of [(1765, 3), 5114, 41]-NRT-code), using OOA 2-folding based on linear OOA(4¹⁸¹, 3530, F₄, 2, 40) (dual of [(3530, 2), 6879, 41]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4¹⁸¹, 3531, F₄, 2, 40) (dual of [(3531, 2), 6881, 41]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(4¹⁸¹, 3531, F₄, 40) (dual of [3531, 3350, 41]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁸¹, 4102, F₄, 40) (dual of [4102, 3921, 41]-code), using
    - 1 times truncation [i] based on linear OA(4¹⁸², 4103, F₄, 41) (dual of [4103, 3921, 42]-code), using
      - constructionÂ X applied to C_e(40) âŠ‚ C_e(38) [i] based on
        linear OA(4¹⁸¹, 4096, F₄, 41) (dual of [4096, 3915, 42]-code), using an extension C_e(40) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 4⁶âˆ’1, defining interval IÂ =Â [1,40], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 41 [i]
        linear OA(4¹⁷⁵, 4096, F₄, 39) (dual of [4096, 3921, 40]-code), using an extension C_e(38) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 4⁶âˆ’1, defining interval IÂ =Â [1,38], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 39 [i]
        linear OA(4¹, 7, F₄, 1) (dual of [7, 6, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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.