MinT - Information on Result #1543992

Information on Result #1543992

Linear OOA(4²³¹, 465185, F₄, 3, 30) (dual of [(465185, 3), 1395324, 31]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4²³¹, 465185, F₄, 2, 30) (dual of [(465185, 2), 930139, 31]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4²³¹, 524313, F₄, 2, 30) (dual of [(524313, 2), 1048395, 31]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4²²⁹, 524312, F₄, 2, 30) (dual of [(524312, 2), 1048395, 31]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4²²⁹, 1048624, F₄, 30) (dual of [1048624, 1048395, 31]-code), using
    - constructionÂ X applied to C_e(29) âŠ‚ C_e(24) [i] based on
      1. linear OA(4²²¹, 1048576, F₄, 30) (dual of [1048576, 1048355, 31]-code), using an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
      2. linear OA(4¹⁸¹, 1048576, F₄, 25) (dual of [1048576, 1048395, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [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(4²³¹, 93036, F₄, 33, 30) (dual of [(93036, 33), 3069957, 31]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row