# Liner Code over IntegerRing

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I want to make linear code over ring that is not field. I try to do this

sage: MS = MatrixSpace(IntegerModRing(4),3,3);
sage: G = MS([[1,0,0],[0,1,0],[0,0,1]])
sage: C=LinearCode(G)


But, there is error such as below

NotImplementedError: Echelon form not implemented over 'Ring of integers modulo 4'


Of course, there is no problem if I use IntegerModRing(n) with prime number n, but it is ring that is also field. I hope I can make Linear Code over Ring. Could somebody help me? Thanks.

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Hello,

It does not seem to be supported. There is no support for submodules of $\mathbb{Z} / n \mathbb{Z}$

sage: F = Zmod(4)**3
sage: v0 = F((1,0,0))
sage: v1 = F((1,1,1))
sage: F.submodule([v0,v1])
Traceback (most recent call last):
...
NotImplementedError: Echelon form not implemented over 'Ring of integers modulo 4'.


There is an old ticket (#6452) on the Sage development website that aimed to implement it. There is some code with it but sadly not in final stage. If you have some programming skill you might have a look and contribute to Sage!

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Ok. Thanks.

( 2015-10-07 21:08:16 -0500 )edit