更仔细地看看实际可用的内容：

edd@max:~$ apt-cache search mingw-
libassuan-mingw-w64-dev - IPC library for the GnuPG components -- Windows port
libgcrypt-mingw-w64-dev - LGPL Crypto library - Windows development
libgpg-error-mingw-w64-dev - library of error values and messages in GnuPG (Windows development)
libksba-mingw-w64-dev - X.509 and CMS support library (Windows development)
libnpth-mingw-w64-dev - replacement for GNU Pth using system threads (Windows dev)
binutils-mingw-w64 - Cross-binutils for Win32 and Win64 using MinGW-w64
binutils-mingw-w64-i686 - Cross-binutils for Win32 (x86) using MinGW-w64
binutils-mingw-w64-x86-64 - Cross-binutils for Win64 (x64) using MinGW-w64
g++-mingw-w64 - GNU C++ compiler for MinGW-w64
g++-mingw-w64-i686 - GNU C++ compiler for MinGW-w64 targeting Win32
g++-mingw-w64-x86-64 - GNU C++ compiler for MinGW-w64 targeting Win64
gcc-mingw-w64 - GNU C compiler for MinGW-w64
gcc-mingw-w64-base - GNU Compiler Collection for MinGW-w64 (base package)
gcc-mingw-w64-i686 - GNU C compiler for MinGW-w64 targeting Win32
gcc-mingw-w64-x86-64 - GNU C compiler for MinGW-w64 targeting Win64
gdb-mingw-w64 - Cross-debugger for Win32 and Win64 using MinGW-w64
gdb-mingw-w64-target - Cross-debugger server for Win32 and Win64 using MinGW-w64
gfortran-mingw-w64 - GNU Fortran compiler for MinGW-w64
gfortran-mingw-w64-i686 - GNU Fortran compiler for MinGW-w64 targeting Win32
gfortran-mingw-w64-x86-64 - GNU Fortran compiler for MinGW-w64 targeting Win64
gnat-mingw-w64 - GNU Ada compiler for MinGW-w64
gnat-mingw-w64-base - GNU Ada compiler for MinGW-w64 (base package)
gnat-mingw-w64-i686 - GNU Ada compiler for MinGW-w64 targeting Win32
gnat-mingw-w64-x86-64 - GNU Ada compiler for MinGW-w64 targeting Win64
gobjc++-mingw-w64 - GNU Objective-C++ compiler for MinGW-w64
gobjc++-mingw-w64-i686 - GNU Objective-C++ compiler for MinGW-w64 targeting Win32
gobjc++-mingw-w64-x86-64 - GNU Objective-C++ compiler for MinGW-w64 targeting Win64
gobjc-mingw-w64 - GNU Objective-C compiler for MinGW-w64
gobjc-mingw-w64-i686 - GNU Objective-C compiler for MinGW-w64 targeting Win32
gobjc-mingw-w64-x86-64 - GNU Objective-C compiler for MinGW-w64 targeting Win64
libz-mingw-w64 - compression library - Windows runtime
libz-mingw-w64-dev - compression library - Windows development files
mingw-ocaml - ocaml-mingw-w64 transitional dummy package
mingw-w64 - Development environment targeting 32- and 64-bit Windows
mingw-w64-common - Common files for Mingw-w64
mingw-w64-i686-dev - Development files for MinGW-w64 targeting Win32
mingw-w64-tools - Development tools for 32- and 64-bit Windows
mingw-w64-x86-64-dev - Development files for MinGW-w64 targeting Win64
ocaml-mingw-w64 - OCaml cross-compiler based on mingw -- Meta-package
ocaml-mingw-w64-i686 - OCaml cross-compiler based on mingw -- 32 bit compiler
ocaml-mingw-w64-x86-64 - OCaml cross-compiler based on mingw -- 64 bit compiler
edd@max:~$

所以sudo apt-get install gcc-mingw-w64可能就是您想要的，您应该通过设置适当的编译器选项（可能是-m32）来构建一个32位的可执行文件。

我试过sudo apt-get install gcc-mingw-w64。
然后我用命令编译代码：

i686-w64-mingw32-gcc-win32 input_code.c -o output.exe

如果你在记住编译器的名字上有困难，你可以尝试在linux系统上使用别名，你可以从.bashrc修改
所以mingw的位置在这里-〉/usr/bin/i686-w 64-mingw 32-gcc-win32
在下面你可以创建这样的简化mingw编译器：

alias mingw=/usr/bin/i686-w64-mingw32-gcc-win32