Polar Subcodes

Generalized subspace subcodes with application in cryptology

Most of the codes that have an algebraic decoding algorithm are derived from the Reed Solomon codes. They are obtained by taking equivalent codes, for example the generalized Reed Solomon codes, or by using the so-called subfield subcode method, which leads to Alternant codes and Goppa codes over the underlying prime field, or over some intermediate subfield. The main advantages of these constr...

Galois invariance, trace codes and subfield subcodes

Article history: Received 26 February 2009 Revised 21 September 2009 Available online 2 February 2010 Communicated by W. Cary Huffman

Symmetry Codes and Their Invariant Subcodes

Quasi-cyclic subcodes of cyclic codes

We completely characterize possible indices of quasi-cyclic subcodes in a cyclic code for a very broad class of cyclic codes. We present enumeration results for quasi-cyclic subcodes of a fixed index and show that the problem of enumeration is equivalent to enumeration of certain vector subspaces in finite fields. In particular, we present enumeration results for quasi-cyclic subcodes of the si...

Subspace Subcodes of Reed-Solomon Codes

space subcode of a Reed-Solomon (SSRS) code Over GF(2"') is the set of RS codewords, whose components all lie in a particular GF(2)subspace of GF(2"). SSRS codes include both generalized B C H codes and "trace-shortened" Rs codes [2][3] as special casea. In this paper we present an explicit formula for t h e dimension of an arbitrary RS subspace subcode. Using this formula, we And that in many ...