MinT - Information on Result #1432844

Information on Result #1432844

Linear OOA(4²³⁶, 10947, F₄, 2, 45) (dual of [(10947, 2), 21658, 46]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(4²³⁶, 10947, F₄, 45) (dual of [10947, 10711, 46]-code), using

discarding factors / shortening the dual code based on linear OA(4²³⁶, 16403, F₄, 45) (dual of [16403, 16167, 46]-code), using
- constructionÂ XX applied to C_e(44) âŠ‚ C_e(41) âŠ‚ C_e(40) [i] based on
  1. linear OA(4²³², 16384, F₄, 45) (dual of [16384, 16152, 46]-code), using an extension C_e(44) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,44], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 45 [i]
  2. linear OA(4²¹⁸, 16384, F₄, 42) (dual of [16384, 16166, 43]-code), using an extension C_e(41) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,41], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 42 [i]
  3. linear OA(4²¹¹, 16384, F₄, 41) (dual of [16384, 16173, 42]-code), using an extension C_e(40) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,40], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 41 [i]
  4. linear OA(4³, 18, F₄, 2) (dual of [18, 15, 3]-code), using
    - discarding factors / shortening the dual code based on linear OA(4³, 21, F₄, 2) (dual of [21, 18, 3]-code), using
      - Hamming code H(3,4) [i]
  5. linear OA(4⁰, 1, F₄, 0) (dual of [1, 1, 1]-code), using
    - dual of repetition code with length 1 [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(4²³⁶, 5473, F₄, 3, 45) (dual of [(5473, 3), 16183, 46]-NRT-code)	[i]		OOA Folding