On binary LCD BCH codes of length $ \frac{{{2^m} + 1}}{3} $

Some binary BCH codes with length $n=2^m+1$

Under research for near sixty years, Bose-Ray-Chaudhuri-Hocquenghem(BCH) codes have played increasingly important roles in many applications such as communication systems, data storage and information security. However, the dimension and minimum distance of BCH codes are seldom solved until now because of their intractable characteristics. The objective of this paper is to study the dimensions ...

On the duals of binary BCH codes

We give bounds for the minimal distance of duals of binary BCH codes in a range where the Carlitz-Uchiyama bound is trivial. This is done by estimating the number of points on certain curves over finite fields.

BCH codes of length 511

Parameters of two classes of LCD BCH codes

BCH codes are widely employed in data storage, communications systems, and consumer electronics. A new application of LCD codes in cryptography was found recently. It is known that LCD codes are asymptotically good. LCD cyclic codes were referred to as reversible cyclic codes in the literature. The objective of this paper is to construct a class of LCD codes, which are also BCH codes. The dimen...

New binary and ternary LCD codes

LCD codes are linear codes with important cryptographic applications. Recently, a method has been presented to transform any linear code into an LCD code with the same parameters when it is supported on a finite field with cardinality larger than 3. Hence, the study of LCD codes is mainly open for binary and ternary fields. Subfield-subcodes of $J$-affine variety codes are a generalization of B...