The Codes Over ℤ₄ Package

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Codes Over ℤ₄ is a package that expand the current functionality for codes over ℤ₄ in Magma. Specifically, there are functions which give new constructions for some families of codes over ℤ₄ and constructions to obtain new codes over ℤ₄ from given codes over ℤ₄. Moreover, efficient functions for computing the rank and dimension of the kernel of any code over ℤ₄ are also include, as well as general functions to compute the coset leaders for a subcode in a code over ℤ₄. Finally, there are also functions to compute the permutation automorphism group for Hadamard and extended perfect codes over ℤ₄, and their cardinal.

Codes Over ℤ₄ consists of one file written in the Magma language. Please send your bug reports to Combinatorics, Coding and Security Group (CCSG) at [email protected] or if it is a Magma problem to magma-trouble ([email protected]). See the section below.

Codes Over ℤ₄ was originally written in Magma by Jaume Pernas (supervised by Mercè Villanueva and Jaume Pujol) as a support for a research project on ℤ₄-Linear codes developed by the Combinatorics, Coding and Security Group (CCSG) within the Department of Information and Communications Engineering (dEIC) at the Autonomous University of Barcelona (UAB).

Composition of the package

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The Codes Over ℤ₄ package is composed of four directories:

• /src: The file to attach to Magma CodesOverZ4.m.
• /doc: The manual to use the package in pdf format.
• /test: A sample code that tests the package. They can be loaded in Magma as soon as the package is attached.
• /examples: Examples from the manual. They can be loaded in Magma as soon as the package is attached.

Using/Installing Codes Over ℤ₄

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Since Magma version 2.15-15 part of this package is included in magma default functions and it is not necessary to be installed. However, for older versions and for new functions the package can be installed as we show:

To use Codes Over ℤ₄ temporally (as a Magma Package) unpack the archive file in a directory. Enter to the ./src directory. Call Magma and then write:

> Attach("CodesOverZ4.m");

Install Codes Over ℤ₄ permanent (as a Magma Package):

1. Unpack the archive file in a directory.

2. Enter to the directory where Magma is installed, go to package directory $PATHMAGMA/package/ and create a new directory.

   > mkdir CodesOverZ4

3. Copy the source code file

   > cp $PATH/src/CodesOverZ4.m $PATHMAGMA/package/CodesOverZ4/

4. Edit the file $PATHMAGMA/package/spec and write the following lines at the end:

   CodesOverZ4
   {
      CodesOverZ4.m
   }
   

Bug Reports

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When sending a bug report to [email protected] or to [email protected], remember we will need to be able to reproduce the problem; so please include:

• The version of Magma you are using; either look at the header when you start up Magma.
• The operating system you are using e.g. Linux, SunOS 5.8 = Solaris 2.8, IRIX 6.5, Windows, ...
• A script that demonstrates the bug, along with a description of why it's a bug (e.g. by adding comments to the script
  • recall comments in Magma begin with a // or between /* */).

March 5, 2012