MinT - Information on Result #1543902

Information on Result #1543902

Linear OOA(4²³⁰, 1713194, F₄, 3, 27) (dual of [(1713194, 3), 5139352, 28]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4²³⁰, 1713194, F₄, 2, 27) (dual of [(1713194, 2), 3426158, 28]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4²³⁰, 2097178, F₄, 2, 27) (dual of [(2097178, 2), 4194126, 28]-NRT-code), using
- 4¹ times duplication [i] based on linear OOA(4²²⁹, 2097178, F₄, 2, 27) (dual of [(2097178, 2), 4194127, 28]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4²²⁹, 4194356, F₄, 27) (dual of [4194356, 4194127, 28]-code), using
    - constructionÂ X applied to C_e(26) âŠ‚ C_e(21) [i] based on
      1. linear OA(4²²¹, 4194304, F₄, 27) (dual of [4194304, 4194083, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
      2. linear OA(4¹⁷⁷, 4194304, F₄, 22) (dual of [4194304, 4194127, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
      3. linear OA(4⁸, 52, F₄, 4) (dual of [52, 44, 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(4²³⁰, 342638, F₄, 33, 27) (dual of [(342638, 33), 11306824, 28]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row