2,872 research outputs found
On quadratic residue codes and hyperelliptic curves
A long standing problem has been to develop "good" binary linear codes to be
used for error-correction. This paper investigates in some detail an attack on
this problem using a connection between quadratic residue codes and
hyperelliptic curves. One question which coding theory is used to attack is:
Does there exist a c<2 such that, for all sufficiently large and all
subsets S of GF(p), we have |X_S(GF(p))| < cp?Comment: 18 pages, no figure
A new class of three-weight linear codes from weakly regular plateaued functions
Linear codes with few weights have many applications in secret sharing
schemes, authentication codes, communication and strongly regular graphs. In
this paper, we consider linear codes with three weights in arbitrary
characteristic. To do this, we generalize the recent contribution of Mesnager
given in [Cryptography and Communications 9(1), 71-84, 2017]. We first present
a new class of binary linear codes with three weights from plateaued Boolean
functions and their weight distributions. We next introduce the notion of
(weakly) regular plateaued functions in odd characteristic and give
concrete examples of these functions. Moreover, we construct a new class of
three-weight linear -ary codes from weakly regular plateaued functions and
determine their weight distributions. We finally analyse the constructed linear
codes for secret sharing schemes.Comment: The Extended Abstract of this work was submitted to WCC-2017 (the
Tenth International Workshop on Coding and Cryptography
A Method to determine Partial Weight Enumerator for Linear Block Codes
In this paper we present a fast and efficient method to find partial weight
enumerator (PWE) for binary linear block codes by using the error impulse
technique and Monte Carlo method. This PWE can be used to compute an upper
bound of the error probability for the soft decision maximum likelihood decoder
(MLD). As application of this method we give partial weight enumerators and
analytical performances of the BCH(130,66), BCH(103,47) and BCH(111,55)
shortened codes; the first code is obtained by shortening the binary primitive
BCH (255,191,17) code and the two other codes are obtained by shortening the
binary primitive BCH(127,71,19) code. The weight distributions of these three
codes are unknown at our knowledge.Comment: Computer Engineering and Intelligent Systems Vol 3, No.11, 201
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