MinT - Information on Result #2222083

Information on Result #2222083

Linear OA(2¹¹⁸, 154, F₂, 42) (dual of [154, 36, 43]-code), using 1 times truncation based on linear OA(2¹¹⁹, 155, F₂, 43) (dual of [155, 36, 44]-code), using

constructionÂ X applied to C_e(42) âŠ‚ C_e(30) [i] based on
1. linear OA(2⁹⁹, 128, F₂, 43) (dual of [128, 29, 44]-code), using an extension C_e(42) of the primitive narrow-sense BCH-code C(I) with length 127Â = 2⁷âˆ’1, defining interval IÂ =Â [1,42], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 43 [i]
2. linear OA(2⁹², 128, F₂, 31) (dual of [128, 36, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 127Â = 2⁷âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
3. linear OA(2²⁰, 27, F₂, 11) (dual of [27, 7, 12]-code), using
  - residual code [i] based on linear OA(2⁴³, 51, F₂, 23) (dual of [51, 8, 24]-code), using
    - concatenation of two codes [i] based on
      1. linear OA(4¹³, 17, F₄, 11) (dual of [17, 4, 12]-code), using
        projective code from ovoid in PG(3,Â 4) [i]
      2. linear OA(2¹, 3, F₂, 1) (dual of [3, 2, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]

Mode: Constructive and 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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2¹¹⁸, 77, F₂, 2, 42) (dual of [(77, 2), 36, 43]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2¹¹⁸, 51, F₂, 3, 42) (dual of [(51, 3), 35, 43]-NRT-code)	[i]		OOA Folding