MinT - Information on Result #1420483

Information on Result #1420483

Linear OOA(4⁶⁷, 4185625, F₄, 2, 8) (dual of [(4185625, 2), 8371183, 9]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(4⁶⁷, 4185625, F₄, 8) (dual of [4185625, 4185558, 9]-code), using

discarding factors / shortening the dual code based on linear OA(4⁶⁷, 4194316, F₄, 8) (dual of [4194316, 4194249, 9]-code), using
- 1 times truncation [i] based on linear OA(4⁶⁸, 4194317, F₄, 9) (dual of [4194317, 4194249, 10]-code), using
  - constructionÂ X4 applied to C_e(8) âŠ‚ C_e(6) [i] based on
    1. linear OA(4⁶⁷, 4194304, F₄, 9) (dual of [4194304, 4194237, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
    2. linear OA(4⁵⁶, 4194304, F₄, 7) (dual of [4194304, 4194248, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
    3. linear OA(4¹², 13, F₄, 12) (dual of [13, 1, 13]-code or 13-arc in PG(11,4)), using
      - dual of repetition code with length 13 [i]
    4. linear OA(4¹, 13, F₄, 1) (dual of [13, 12, 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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4⁶⁷, 2092812, F₄, 3, 8) (dual of [(2092812, 3), 6278369, 9]-NRT-code)	[i]		OOA Folding
2	Linear OOA(4⁶⁷, 2092812, F₄, 10, 8) (dual of [(2092812, 10), 20928053, 9]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row