MinT - Information on Result #680672

Information on Result #680672

Linear OA(4²⁵⁴, 1057, F₄, 67) (dual of [1057, 803, 68]-code), using constructionÂ X applied to C_e(68) âŠ‚ C_e(58) based on

linear OA(4²⁴¹, 1024, F₄, 69) (dual of [1024, 783, 70]-code), using an extension C_e(68) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 4⁵âˆ’1, defining interval IÂ =Â [1,68], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 69 [i]
linear OA(4²²¹, 1024, F₄, 59) (dual of [1024, 803, 60]-code), using an extension C_e(58) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 4⁵âˆ’1, defining interval IÂ =Â [1,58], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 59 [i]
linear OA(4¹³, 33, F₄, 7) (dual of [33, 20, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(4¹³, 34, F₄, 7) (dual of [34, 21, 8]-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OA(4⁴, 17, F₄, 3) (dual of [17, 13, 4]-code or 17-cap in PG(3,4)), using
      - ovoid in PG(3,Â 4) [i]
    2. linear OA(4⁹, 17, F₄, 7) (dual of [17, 8, 8]-code), using
      - dual code (with bound on d by constructionÂ Y1) [i] based on
        linear OA(4⁸, 17, F₄, 6) (dual of [17, 9, 7]-code), using
        the BCH-code C(I) with length 17Â | 4⁴âˆ’1, defining interval IÂ =Â {1,4,7,…,16}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        nonexistence of linear OA(4⁷, 10, F₄, 6) (dual of [10, 3, 7]-code), because
        bound for almost-MDS-codes with dimension nÂ =Â 3 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4²⁵⁴, 528, F₄, 2, 67) (dual of [(528, 2), 802, 68]-NRT-code)	[i]		OOA Folding
2	Linear OOA(4²⁵⁴, 352, F₄, 3, 67) (dual of [(352, 3), 802, 68]-NRT-code)	[i]		OOA Folding