Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8895624 | Finite Fields and Their Applications | 2018 | 11 Pages |
Abstract
We consider the extendability of linear codes over F4, the field of order four. Let C be [n,k,d]4 code with dâ¡1(mod4), kâ¥3. The weight spectrum modulo 4 (4-WS) of C is defined as the ordered 4-tuple (w0,w1,w2,w3) with w0=13â4|i>0Ai, wj=13âiâ¡j(mod4)Ai for j=1,2,3. We prove that C is 3-extendable if w0+w2=θkâ2 and if either (a) w1âw0<4kâ2+4âθkâ3; (b) w1âw0>10â
4kâ3âθkâ3 or (c) (w0,w1)=(θkâ3,6â
4kâ3). We also give a sufficient condition for the l-extendability of [n,k,d]4 codes with dâ¡4âl(mod4), kâ¥3 for l=1,2,3 when w0+w2=θkâ2+2â
4kâ2.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
H. Kanda, T. Maruta,