MinT - Information on Result #1539406

Information on Result #1539406

Linear OOA(4¹⁷⁴, 163707, F₄, 3, 24) (dual of [(163707, 3), 490947, 25]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(4¹⁷⁴, 163707, F₄, 24) (dual of [163707, 163533, 25]-code), using

discarding factors / shortening the dual code based on linear OA(4¹⁷⁴, 262200, F₄, 24) (dual of [262200, 262026, 25]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4¹⁷³, 262199, F₄, 24) (dual of [262199, 262026, 25]-code), using
  - constructionÂ X applied to C_e(24) âŠ‚ C_e(17) [i] based on
    1. linear OA(4¹⁶³, 262144, F₄, 25) (dual of [262144, 261981, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
    2. linear OA(4¹¹⁸, 262144, F₄, 18) (dual of [262144, 262026, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
    3. linear OA(4¹⁰, 55, F₄, 5) (dual of [55, 45, 6]-code), using
      - discarding factors / shortening the dual code based on linear OA(4¹⁰, 63, F₄, 5) (dual of [63, 53, 6]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 4³âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [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(4¹⁷⁴, 40926, F₄, 27, 24) (dual of [(40926, 27), 1104828, 25]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row