What Kind Of Field Is The Bch A Subfield

Last Updated on May 16, 2023 by Paganoto

BCH codes

The subfield subcode C|q consists of all codewords of C, whose coordinates belong to GF(q). Proposition. Let C be a [n, k, d]qm code (over the field GF(qm)).

Finite field – Wikipedia

Finite fields are fundamental in a number of areas of mathematics and computer science, including number theory, algebraic geometry, Galois theory, finite …

Reed-Solomon, BCH, Reed-Muller, and concatenated codes

Reed-Solomon codes are a family of codes defined over large fields as follows. … Corollary 7 BCH codes are subfield subcodes of Reed-Solomon codes.

Extending and Lengthening BCH Codes – ScienceDirect.com

by J Bierbrauer · 1997 · Cited by 22 — As the one-point truncations of Reed–Solomon subfield codes are precisely the primitive BCH codes it is natural to extend our study to BCH codes in general.

The subfield codes and subfield subcodes of a family of MDS …

by C Tang · 2021 · Cited by 2 — BCH code, cyclic code, MDS code, subfield code, subfield subcode, t-design. … CYCLIC CODES AND BCH CODES OVER FINITE FIELDS.

The subfield codes and subfield subcodes of a family of MDS codes …

Ii Cyclic codes and BCH codes over finite fields. Let q be a prime power. An [n,k,d] code C over GF(q) is said to be cyclic if (c0,c1,⋯,cn−1)∈C implies …

AATA Structure of a Finite Field

The unique finite field with elements is called the Galois field of order . We will denote this field by . GF ( p n ) .

Advances in Algebraic Geometry Codes

Dual BCH codes The RS code of length n = q" –1 with defining set I = {1,2,… … The BCH code over the subfield Fq with the same length and defining set is …

Algebraic Codes on Lines, Planes, and Curves: An Engineering …

Aprimitive BCH code is a subfield-subcode of a primitive Reed– Solomon code. … but the extension field GF(qm) does contain such an element.

Error-correcting Codes – Page 350 – Google Books Result

Q.E.D. 10.6 Polynomial Codes The class of codes called polynomial codes … Q.E.D. As an example of subfield subcodes , note that every ( n , k ) BCH code …

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