MinT - Information on Result #1539682

Information on Result #1539682

Linear OOA(4¹⁷⁸, 44117, F₄, 3, 28) (dual of [(44117, 3), 132173, 29]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(4¹⁷⁸, 44117, F₄, 28) (dual of [44117, 43939, 29]-code), using

discarding factors / shortening the dual code based on linear OA(4¹⁷⁸, 65577, F₄, 28) (dual of [65577, 65399, 29]-code), using
- 1 times truncation [i] based on linear OA(4¹⁷⁹, 65578, F₄, 29) (dual of [65578, 65399, 30]-code), using
  - constructionÂ X applied to C_e(28) âŠ‚ C_e(22) [i] based on
    1. 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]
    2. linear OA(4¹³⁷, 65536, F₄, 23) (dual of [65536, 65399, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
    3. linear OA(4¹⁰, 42, F₄, 5) (dual of [42, 32, 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(4¹⁷⁸, 8823, F₄, 33, 28) (dual of [(8823, 33), 290981, 29]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row