论文标题
部分对称单码
Partially symmetric monomial codes
论文作者
论文摘要
考虑了单一代码的框架，其中包括通过评估某些单一元素生成的线性代码。极性和芦苇毛刺代码是此类代码的两个最著名的代表，可以被视为两个极端情况。 Reed-Muller代码具有较大的自动形态组，但其低复杂性最大似然解码仍然是一个空旷的问题。另一方面，极地代码的对称性要少得多，但承认有效的近ML解码。我们研究代码对称性与解码效率之间的依赖关系。我们介绍了一个新的代码系列，部分对称单一代码。这些代码的对称性比芦苇毛刺代码较小，并且在“ RM和极地代码之间”之间。引入了其参数的下限以及实现它的显式结构。这些代码的结构特性已被证明，并表明它们通常具有递归结构。
A framework of monomial codes is considered, which includes linear codes generated by the evaluation of certain monomials. Polar and Reed-Muller codes are the two best-known representatives of such codes and can be considered as two extreme cases. Reed-Muller codes have a large automorphism group but their low-complexity maximum likelihood decoding still remains an open problem. On the other hand, polar codes have much less symmetries but admit the efficient near-ML decoding. We study the dependency between the code symmetries and the decoding efficiency. We introduce a new family of codes, partially symmetric monomial codes. These codes have a smaller group of symmetries than the Reed-Muller codes and are in this sense "between" RM and polar codes. A lower bound on their parameters is introduced along with the explicit construction which achieves it. Structural properties of these codes are demonstrated and it is shown that they often have a recursive structure.
