MinT - Information on Result #1539680

Information on Result #1539680

Linear OOA(4¹⁷⁸, 30586, F₄, 3, 30) (dual of [(30586, 3), 91580, 31]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4¹⁷⁸, 30586, F₄, 2, 30) (dual of [(30586, 2), 60994, 31]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4¹⁷⁸, 32772, F₄, 2, 30) (dual of [(32772, 2), 65366, 31]-NRT-code), using
- 4¹ times duplication [i] based on linear OOA(4¹⁷⁷, 32772, F₄, 2, 30) (dual of [(32772, 2), 65367, 31]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4¹⁷⁷, 65544, F₄, 30) (dual of [65544, 65367, 31]-code), using
    - constructionÂ X applied to C_e(29) âŠ‚ C_e(28) [i] based on
      1. linear OA(4¹⁷⁷, 65536, F₄, 30) (dual of [65536, 65359, 31]-code), using an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
      2. linear OA(4¹⁶⁹, 65536, F₄, 29) (dual of [65536, 65367, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
      3. linear OA(4⁰, 8, F₄, 0) (dual of [8, 8, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(4⁰, s, F₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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(4¹⁷⁸, 6117, F₄, 33, 30) (dual of [(6117, 33), 201683, 31]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row