Extended Cyclic Codes Sandwiched Between Reed-Muller Codes
Authors:
- Yan XuYXYan Xu
- Changjiang JiCJChangjiang Ji
- Ran TaoRTRan Tao
- Sihuang HuSHSihuang Hu
Preprint
Abstract
The famous Barnes-Wall lattices can be obtained by applying Construction D to a chain of Reed-Muller codes. By applying Construction ${{D}}^{{(cyc)}}$ to a chain of extended cyclic codes sandwiched between Reed-Muller codes, Hu and Nebe (J. London Math. Soc. (2) 101 (2020) 1068-1089) constructed new series of universally strongly perfect lattices sandwiched between Barnes-Wall lattices. In this paper, we first extend their construction to generalized Reed-Muller codes, and then explicitly determine the minimum vectors of those new sandwiched Reed-Muller codes for some special cases.
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This publication has 13 references indexed in Scilit:
- Reed-Muller Codes PolarizeIEEE Transactions on Information Theory, 2020
- Reed–Muller Codes: Theory and AlgorithmsIEEE Transactions on Information Theory, 2020
- Reed–Muller Codes Achieve Capacity on Erasure ChannelsIEEE Transactions on Information Theory, 2017
- Reed–Muller Codes for Random Erasures and ErrorsIEEE Transactions on Information Theory, 2015
- On generalized ReedMuller codes and their relativesInformation and Control, 1970
- New generalizations of the Reed-Muller codes--I: Primitive codesIEEE Transactions on Information Theory, 1968
- Some results on cyclic codes which are invariant under the affine group and their applicationsInformation and Control, 1967
- Some extreme forms defined in terms of Abelian groupsJournal of the Australian Mathematical Society, 1959
- A class of multiple-error-correcting codes and the decoding schemeTransactions of the IRE Professional Group on Information Theory, 1954
- Application of Boolean algebra to switching circuit design and to error detectionTransactions of the I.R.E. Professional Group on Electronic Computers, 1954