MinT - Information on Result #1478883

Information on Result #1478883

Linear OOA(4⁶⁶, 6179, F₄, 3, 12) (dual of [(6179, 3), 18471, 13]-NRT-code), using OOA 2-folding based on linear OOA(4⁶⁶, 12358, F₄, 2, 12) (dual of [(12358, 2), 24650, 13]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4⁶⁶, 12359, F₄, 2, 12) (dual of [(12359, 2), 24652, 13]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(4⁶⁶, 12359, F₄, 12) (dual of [12359, 12293, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(4⁶⁶, 16401, F₄, 12) (dual of [16401, 16335, 13]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(4⁶⁵, 16400, F₄, 12) (dual of [16400, 16335, 13]-code), using
      - constructionÂ X4 applied to C_e(12) âŠ‚ C_e(9) [i] based on
        linear OA(4⁶⁴, 16384, F₄, 13) (dual of [16384, 16320, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
        linear OA(4⁵⁰, 16384, F₄, 10) (dual of [16384, 16334, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
        linear OA(4¹⁵, 16, F₄, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,4)), using
        dual of repetition code with length 16 [i]
        linear OA(4¹, 16, F₄, 1) (dual of [16, 15, 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.