MinT - Information on Result #1546908

Information on Result #1546908

Linear OOA(4²⁶⁰, 424208, F₄, 3, 34) (dual of [(424208, 3), 1272364, 35]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4²⁶⁰, 424208, F₄, 2, 34) (dual of [(424208, 2), 848156, 35]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4²⁶⁰, 524312, F₄, 2, 34) (dual of [(524312, 2), 1048364, 35]-NRT-code), using
- 4¹ times duplication [i] based on linear OOA(4²⁵⁹, 524312, F₄, 2, 34) (dual of [(524312, 2), 1048365, 35]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4²⁵⁹, 1048624, F₄, 34) (dual of [1048624, 1048365, 35]-code), using
    - constructionÂ X applied to C_e(33) âŠ‚ C_e(28) [i] based on
      1. linear OA(4²⁵¹, 1048576, F₄, 34) (dual of [1048576, 1048325, 35]-code), using an extension C_e(33) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,33], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 34 [i]
      2. linear OA(4²¹¹, 1048576, F₄, 29) (dual of [1048576, 1048365, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
      3. linear OA(4⁸, 48, F₄, 4) (dual of [48, 40, 5]-code), using
        discarding factors / shortening the dual code based on linear OA(4⁸, 85, F₄, 4) (dual of [85, 77, 5]-code), using
        quaternary constacyclic codes with minimum distance 5 [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(4²⁶⁰, 70701, F₄, 39, 34) (dual of [(70701, 39), 2757079, 35]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row