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In coding theory, two q-ary codes are equivalent if one can be obtained from the other by permuting the positions of the code or the symbols in a fixed position.

I know that two equivalent codes have the same parameters (number and length of codewords and minimum distance between codewords) and so when given two codes with differing parameters they obviously are not equivalent.

But when given two codes with the same parameters how can you tell if they are equivalent without actually attempting to find suitable permutations. Or if they are not equivalent, how would you show this?

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    You have to just find suitable permutations, in most cases. There are some other considerations you can use (weight distribution of codewords, etc.) to show they are not equivalent, but if that all fails, you have to use brute force. – 2017-02-11
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    @MorganRodgers Two $[n,k]$ codes with different weight distributions are obviously inequivalent, but it _is_ possible for two codes to have the same weight enumerator and yet be inequivalent. For example, the extended binary quadratic residue code of length $32$ has the same weight enumerator as the binary second-order Reed-Muller code of length $32$ but the weight enumerators of the _cosets_ of these codes are different. – 2017-02-14
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    @DilipSarwate Thank you for the clarification, that is what I was intending to say; that these considerations can be used to show they are *not* equivalent (and that if you can't show they are inequivalent by looking at these invariants, you have to use brute force). – 2017-02-14

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