MinT - Information on Result #1421318

Information on Result #1421318

Linear OOA(4⁹⁷, 909133, F₄, 2, 12) (dual of [(909133, 2), 1818169, 13]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(4⁹⁷, 909133, F₄, 12) (dual of [909133, 909036, 13]-code), using

discarding factors / shortening the dual code based on linear OA(4⁹⁷, 1048612, F₄, 12) (dual of [1048612, 1048515, 13]-code), using
- 2 times code embedding in larger space [i] based on linear OA(4⁹⁵, 1048610, F₄, 12) (dual of [1048610, 1048515, 13]-code), using
  - 1 times truncation [i] based on linear OA(4⁹⁶, 1048611, F₄, 13) (dual of [1048611, 1048515, 14]-code), using
    - constructionÂ X applied to C_e(12) âŠ‚ C_e(8) [i] based on
      1. linear OA(4⁹¹, 1048576, F₄, 13) (dual of [1048576, 1048485, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      2. linear OA(4⁶¹, 1048576, F₄, 9) (dual of [1048576, 1048515, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
      3. linear OA(4⁵, 35, F₄, 3) (dual of [35, 30, 4]-code or 35-cap in PG(4,4)), using
        discarding factors / shortening the dual code based on linear OA(4⁵, 41, F₄, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
        a cap found by Tallinii [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(4⁹⁷, 454566, F₄, 3, 12) (dual of [(454566, 3), 1363601, 13]-NRT-code)	[i]		OOA Folding