Decoding the Ternary (23, 11, 9) Quadratic Residue Code

Decoding the Ternary (23, 11, 9) Quadratic Residue Code

Quadratic residue (QR) codes are cyclic, nominally half-rate codes, that are powerful with respect to their error-correction capabilities. Decoding QR codes is in general a difficult task, but great progress has been made in the binary case since the work of Elia [1] and He et al. [2]. Decoding algorithms for certain nonbinary QR codes were proposed by Higgs and Humphreys in [3] and [4]. In [5]...

Algebraic decoding of the (71, 36, 11) quadratic residue code

In this study, an efficient and fast algebraic decoding algorithm (ADA) for the binary systematic quadratic residue (QR) code of length 73 with the reducible generator polynomial to correct up to six errors is proposed. The S(I, J ) matrix method given by He et al. (2001) is utilised to compute the unknown syndromes S5. A technique called swap base is proposed to correct the weight-4 error patt...

Decoding the (41, 21, 9) Quadratic Residue Code

This paper proposes an algebraic decoding algorithm for the (41, 21, 9) quadratic residue code via Lagrange interpolation formula to determine error check and error locator polynomials. Programs written in C++ language have been executed to check every possible error pattern of this quadratic residue code.

A cyclic weight algorithm of decoding the (47, 24, 11) quadratic residue code

High speed decoding of the binary (47, 24, 11) quadratic residue code

An efficient table lookup decoding algorithm (TLDA) is presented to decode up to five possible errors in a binary systematic (47,24,11) quadratic residue (QR) code. The main idea of the TLDA is based on the weight of syndrome, the syndrome decoder together with a reduced-size lookup table (RSLT), and the shift-search method given by Reed et al. Thus, the size of the lookup table and computation...