Matrix-Product Codes over ? q

  title={Matrix-Product Codes over ? q},
  author={Tim Blackmore and Graham H. Norton},
  journal={Applicable Algebra in Engineering, Communication and Computing},
Codes C 1 ,…,C M of length n over ? q and an M × N matrix A over ? q define a matrix-product code C = [C 1 …C M ] ·A consisting of all matrix products [c 1 … c M ] ·A. This generalizes the (u|u+v)-, (u+v+w|2u+v|u)-, (a+x|b+x|a+b+x)-, (u+v|u-v)- etc. constructions. We study matrix-product codes using Linear Algebra. This provides a basis for a unified analysis of |C|, d(C), the minimum Hamming distance of C, and C ⊥. It also reveals an interesting connection with MDS codes. We determine |C| when… CONTINUE READING
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