Given an [n, k, d]-linear code over a finite field Fq, can you always construct (a)...

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Given an [n, k, d]-linear code over a finite field Fq, can you always construct (a) an [n+1, k+1, d]-linear code? (b) an [n+1, k+1, d]-linear code? (c) an [n-1, k-1, d]-linear code? (d) an [n-1, k+1, d]-linear code? Justify your answer! Given an [n, k, d]-linear code over a finite field Fq, can you always construct (a) an [n+1, k+1, d]-linear code? (b) an [n+1, k+1, d]-linear code? (c) an [n-1, k-1, d]-linear code? (d) an [n-1, k+1, d]-linear code? Justify your answer!

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a Yes we can always construct an n1 k1 dlinear code over Fq One way to do this is to take an n k dlinear code C over Fq and choose a new coordinate wh... View the full answer